Exhibit 10.4

Form of Restricted Share Unit Agreement

(Graded Vesting)

Under the Teradata 2025 New Employee Stock Inducement Plan

You have been awarded a number of restricted share units (the “Share Units”) under the Teradata 2025 New Employee Stock Inducement Plan, as amended from time to time (the “Plan”), as a material inducement to accept employment with Teradata and its affiliate companies (referred to collectively herein as “Teradata”) and pursuant to that certain offer letter entered into by and between you and Teradata. The Share Units are granted upon the terms, and subject to the conditions, set forth in this Restricted Share Unit Agreement (this “Agreement”) and the Plan. Please refer to the restricted share unit information page on the website of Teradata’s third-party Plan administrator for the number of Share Units subject to this Agreement. Capitalized terms used but not otherwise defined herein shall have the meanings ascribed to such terms in the Plan.

1. One-third of the Share Units will become vested on each of the first three anniversaries of the date of grant of this award (the “Date of Grant”, and each such anniversary thereof a “Vesting Date”), subject to such rounding conventions as may be implemented from time-to-time by the third party Plan administrator, and provided that you are continuously employed by Teradata until each such Vesting Date.

2. If your employment with Teradata terminates prior to a Vesting Date due to (i) your death, or (ii) a disability for which you qualify for benefits under the Teradata Long-Term Disability Plan or another long-term disability plan sponsored by Teradata (“Disability”), then, upon such termination of employment, the remaining unvested Share Units will become fully vested.

If your employment with Teradata terminates prior to a Vesting Date due to your Retirement, then the Compensation and People Committee of the Teradata Board of Directors (the “Committee”) or its delegate, may in its sole discretion choose to provide that all or any pro rata portion of the Share Units will become vested upon the terms, and subject to the conditions, established by the Committee, including the acceleration of up to one year of vesting for Share Units. For purposes of this Agreement, “Retirement” means termination by you of your employment with Teradata (for any reason other than termination by Teradata for Cause) at or after age 55.

If your employment with Teradata is terminated prior to a Vesting Date due to a reduction-in-force, then, upon such termination of employment, a pro rata portion of the Share Units will become fully vested. The pro rata portion of the Share Units that will become fully vested will be determined by multiplying (x) the number of unvested Share Units that would have vested on the next Vesting Date had you remained employed with Teradata by (y) a fraction, the numerator of which is the number of full and partial months of employment you completed commencing with the Vesting Date that occurred immediately prior to your termination (or, if none, commencing on the Date of Grant), and the denominator of which is twelve (12) months (subject to such rounding conventions as may be implemented from time-to-time by the third party Plan administrator). For purposes of determining such pro rata vesting of your Share Units, your period of employment with Teradata shall not include any leave of absence, other than an approved leave of absence from which Teradata reasonably expects that you will return to perform services for Teradata. Teradata in its sole discretion determines when an employee’s position is terminated due to a reduction-in-force.

Notwithstanding any provision in this Agreement to the contrary, in the event of a Change in Control, the applicable provisions of Section 20 of the Plan shall govern the treatment of your outstanding Share Units as provided therein.

To the extent that the Share Units are not vested pursuant to Sections 1 and 2 above, then except as may otherwise be provided in a severance plan maintained by Teradata and applicable to you, they shall be forfeited automatically without further action or notice, if you cease to be employed by Teradata prior to an applicable Vesting Date other than as provided pursuant to this Section 2.

3. Except as may be otherwise provided in this Agreement, when vested, the Share Units will be paid to you within 30 days after each applicable Vesting Date (or such earlier date as the Share Units may become vested pursuant to Section 2 above) in Shares (such that one Share Unit equals one Share).

4. By accepting this award, unless disclosure is required or permitted by Applicable Law, you agree to keep this Agreement confidential and not to disclose its contents to anyone except your attorney, your immediate family, or your financial consultant, provided such persons agree in advance to keep such information confidential and not disclose it to others. The Share Units will be forfeited if you violate the terms and conditions of this Section 4. Notwithstanding the foregoing, nothing contained in this Agreement or any other Teradata agreement, policy, practice, procedure, directive or instruction shall prohibit you from reporting possible violations of federal, state or local laws or regulations to any federal, state or local governmental agency or commission (a “Government Agency”), from making other disclosures that are protected under the whistleblower provisions of federal, state or local laws or regulations or from exercising any rights you may have under Section 7 of the National Labor Relations Act. You do not need prior authorization of any kind to make any such reports or disclosures and you are not required to notify Teradata that you have made such reports or disclosures. Nothing in this Agreement limits any right you may have to receive a whistleblower award or bounty for information provided to any Government Agency.

5. The Share Units may not be sold, transferred, pledged, assigned or otherwise alienated, except by beneficiary designation, will or by the laws of descent and distribution upon your death. As soon as practicable after the date that the Share Units become vested, Teradata will instruct its transfer agent and/or its third-party Plan administrator to record on your account the number of Shares underlying the number of Share Units to be paid to you in Shares and such Shares will be freely transferable.

6. Any cash dividends declared on the Shares underlying unvested Share Units shall not be paid currently but shall be converted into additional Share Units. Any Share Units resulting from such conversion (the “Dividend Units”) will be considered Share Units for purposes of this Agreement and will be subject to all of the terms, conditions and restrictions set forth herein, including the applicable vesting schedule. As of each date that Teradata would otherwise pay the declared dividend on the Shares underlying unvested Share Units (the “Dividend Payment Date”) in the absence of the reinvestment requirements of this Section 6, the number of Dividend Units will be determined by dividing the amount of dividends otherwise attributable to the unvested Share Units but not paid on the Dividend Payment Date by the Fair Market Value of Teradata’s common stock on the Dividend Payment Date.

7. Teradata has the right to deduct or cause to be deducted, or collect or cause to be collected, with respect to the taxation of any Share Units, the issuance or sale of Shares, and the receipt of dividends or dividend equivalents, if any, or otherwise in relation to you participation in the Plan, any federal, state, local, foreign or other taxes, social contributions, required deductions, or other payments required by the laws of the United States or any other country to be withheld or paid with respect to the Share Units or related to or resulting from your participation in the Plan (“Tax-Related Items”), and you or your legal representative or beneficiary will be required to pay any such amounts. By accepting this award, you consent and direct that, if you are paid through Teradata’s United States payroll system at the time the

Share Units are settled, Teradata’s stock plan administrator will withhold or sell the number of Shares underlying the Share Units as Teradata, in its sole discretion, deems necessary to satisfy such Tax-Related Items; provided, however, that if Teradata is required to withhold any taxes prior to settlement of the Share Units, then you agree that Teradata may satisfy those withholding obligations by withholding cash from your compensation otherwise due to you or by any other action as it may deem necessary to satisfy the withholding obligation. In no event shall the value of the Shares of common stock to be surrendered pursuant to this Section 7 to satisfy applicable withholding taxes (as determined by Teradata) exceed the minimum amount of taxes required to be withheld or such other amount that will not result in a negative accounting impact. If you are paid through a non-United States Teradata payroll system, you agree that Teradata may satisfy any Tax-Related Items by withholding cash from your compensation otherwise due to you or by any other action as it may deem necessary to satisfy the Tax-Related Items. Regardless of any action Teradata or your employer (the “Employer”) takes with regards to any Tax-Related Items, you acknowledge that the ultimate liability for all Tax-Related Items is and remains your responsibility and may exceed the amount actually withheld by Teradata or the Employer. You also agree that you solely are responsible for filing all relevant documentation that may be required of you in relation to this award or any Tax-Related Items, such as but not limited to personal income tax returns or reporting statements in relation to the grant or vesting of this award or the subsequent sale of Shares acquired pursuant to such award and the receipt of any dividends or dividend equivalents.

8. The Share Units shall be subject to Section 19(a) of the Plan if your employment is terminated by Teradata for Cause. This means that, upon termination of your employment for Cause, (a) your Share Units (whether or not vested) will be forfeited automatically and without further action or notice, and (b) to the extent demanded by the Committee in its sole discretion and permitted by Applicable Law, you shall (i) return to Teradata all Shares that you have not disposed of that have been acquired pursuant to this Agreement during the two (2) years prior to the date of your termination of employment, and (ii) with respect to any Shares acquired pursuant to this Agreement during the two (2) years prior to the date of your termination of employment and that you have disposed of, pay to Teradata in cash the Fair Market Value of such Shares, determined as of the date acquired.

9. As a recipient of this equity award, you recognize that you have access to highly confidential, proprietary and non-public information of Teradata and its customers, including strategic plans, customer lists, research and development plans, and other information not made available to the general public and from which Teradata derives value. For purposes of this Agreement, this information is defined as “Trade Secret Information.”

To protect Teradata’s investment in Trade Secret Information, and in exchange for the Share Units, you agree that the following restrictions will apply during your employment with Teradata and, to the extent permitted by Applicable Law, for a period of twelve (12) months after the date that you cease to be employed by Teradata for any reason (the “Termination Date”) (or if Applicable Law mandates a maximum time that is shorter than twelve months, then for a period of time equal to that shorter maximum period):

(a) You will not, without the prior written consent of the Chief Executive Officer of Teradata, render services directly or indirectly to, or become employed by, any Competing Organization of Teradata (as defined in this Section 9 below) to the extent such services or employment involves the development, manufacture, marketing, sale, advertising or servicing of any product, process, system or service which is the same or similar to, or competes with, a product, process, system or service manufactured, sold, marketed, serviced or otherwise provided by Teradata to its customers and upon which you worked or in which you participated during the last twelve (12) months of your Teradata employment. (This restriction

is specifically intended to protect the value of and Teradata’s investment in Trade Secret Information to which you had access as an employee of Teradata). NOTWITHSTANDING THE FOREGOING, THE RESTRICTION SET FORTH IN THIS SECTION 9(a) SHALL NOT APPLY IF YOU ARE EMPLOYED BY TERADATA IN CALIFORNIA, NORTH DAKOTA, OKLAHOMA AND THE DISTRICT OF COLUMBIA OR ANY STATE WHICH ENACTS LEGISLATION PROHIBITING SUCH AGREEMENTS.

(b) You will not, without the prior written consent of the Chief Executive Officer of Teradata, directly or indirectly recruit, hire, solicit or induce, or attempt to induce, any exempt employee of Teradata to terminate his or her employment with or otherwise cease his or her relationship with Teradata. (This restriction is specifically intended to protect the value of the information you obtained while a Teradata employee regarding the skills, experience and knowledge of Teradata employees, which is Trade Secret Information, and Teradata’s investment in developing these employees). NOTWITHSTANDING THE FOREGOING, THE RESTRICTION SET FORTH IN THIS SECTION 9(b) SHALL NOT APPLY IF YOU ARE EMPLOYED BY TERADATA IN CALIFORNIA, NORTH DAKOTA, OKLAHOMA AND THE DISTRICT OF COLUMBIA OR ANY STATE WHICH ENACTS LEGISLATION PROHIBITING SUCH AGREEMENTS.

(c) You will not, without the prior written consent of the Chief Executive Officer of Teradata, solicit the business of any firm or company with which you worked during the preceding twelve (12) months of employment at Teradata, if such firm or company was a customer of Teradata, by using Teradata Trade Secret Information. (This restriction is specifically intended to protect the value of the identity of Teradata customers, their needs, interests, strategic plans, etc., all of which is Trade Secret Information you acquired as a Teradata employee with access to such information).

If you breach the terms of this Section 9, you agree that in addition to any liability you may have for damages arising from such breach, your Share Units (whether or not vested) will be forfeited automatically and without further action or notice, and, to the extent permitted by Applicable Law, with respect to any Shares acquired pursuant to this Agreement during the twelve (12) months prior to the Termination Date, you agree to pay to Teradata in cash the Fair Market Value of such Shares, determined as of the date acquired.

As used in this Section 9, “Competing Organization” means a person or organization which is engaged in or about to become engaged in research on or development, production, marketing, leasing, selling or servicing of a product, process, system or service which is the same or similar to and competes with a product, process, system or service manufactured, sold, serviced or otherwise provided by Teradata to its customers and is therefore a competitor of Teradata.

10. By accepting this award, you agree that, where permitted by local law, any controversy or claim arising out of or related to this Agreement or your employment relationship with Teradata shall be resolved by first exhausting Teradata’s internal dispute resolution process and policy in place when the dispute arose, and then by arbitration pursuant the Mutual Agreement to Arbitrate All Employment Related Claims attached hereto as Exhibit A.

Notwithstanding the preceding subparagraph, you acknowledge that if you breach Section 9, Teradata will sustain irreparable injury and will not have an adequate remedy at law. As a result, you agree that in the event of your breach of Section 9 Teradata may, in addition to any other remedies available to it, bring an action in a court of competent jurisdiction for equitable relief to preserve the status quo pending appointment of an arbitrator and completion of an arbitration.

11. You may designate one or more beneficiaries to receive all or part of any Share Units to be distributed in case of your death, and you may change or revoke such designation at any time. In the event of your death, any Share Units distributable hereunder that are subject to such a designation will be distributed to such beneficiary or beneficiaries in accordance with this Agreement. Any other Share Units not designated by you will be distributable to your estate. If there is any question as to the legal right of any beneficiary to receive a distribution hereunder, the Share Units in question may be transferred to your estate, in which event Teradata will have no further liability to anyone with respect to such Share Units.

12. The provisions of this Agreement are severable. If any provision of this Agreement is held to be unenforceable or invalid by a court or other tribunal of competent jurisdiction (including an arbitration tribunal), it shall be severed and shall not affect any other part of this Agreement, which will be enforced as permitted by law.

13. Subject to Section 21 of the Plan, the terms of this award of Share Units as evidenced by this Agreement may be amended by the Teradata Board of Directors or the Committee at any time.

14. The number of Share Units and the number and kind of Shares covered by this Agreement shall be subject to adjustment as provided in Section 15 of the Plan.

15. In the event of a conflict between the terms and conditions of this Agreement and the terms and conditions of the Plan, the terms and conditions of the Plan shall prevail, except that with respect to matters involving choice of law the terms and conditions of Section 10 of this Agreement shall prevail.

16. You shall not possess any incidents of ownership (including, without limitation, dividend and voting rights) in the Shares underlying the Share Units until such Shares have been delivered to you in accordance with this Agreement. The obligations of Teradata under this Agreement will be merely that of an unfunded and unsecured promise of Teradata to deliver Shares in the future following vesting of the Share Units, and your rights will be no greater than those of an unsecured general creditor. No assets of Teradata will be held or set aside as security for the obligations of Teradata under this Agreement.

17. The intent of the parties is that payments under this Agreement be exempt from, or comply with, Section 409A of the Code, and this Agreement shall be interpreted, administered and governed in accordance with such intent. In particular, solely to the extent necessary to comply with Section 409A of the Code: (x) a “termination of employment” or words of similar effect shall be deemed to mean a “separation from service” within the meaning of Section 409A of the Code, and (y) payment of any nonqualified deferred compensation to a “specified employee” (as determined under applicable Teradata policy) shall be made no earlier than the first business day that is more than six months after the date of separation from service. Further, notwithstanding anything to the contrary contained in this Agreement, the Committee shall have the right, at any time in its sole discretion, to accelerate the time of a payment under this Agreement to a time otherwise permitted under Section 409A of the Code in accordance with the requirements, restrictions and limitations of Treasury Regulation Section 1.409A-3(j), to the extent applicable.

18. Nothing contained in this Agreement shall confer upon you any right with respect to continuance of employment by Teradata, nor limit or affect in any manner the right of Teradata to terminate your employment or adjust your compensation.

19. By accepting any benefit under this Agreement, you and each person claiming under or through you shall be conclusively deemed to have indicated their acceptance and ratification of, and consent to, all of the terms and conditions of this Agreement and the Plan and any action taken under this Agreement or

the Plan by the Committee, the Board of Directors or Teradata, in any case in accordance with the terms and conditions of this Agreement.

20. Teradata may, in its sole discretion, decide to deliver any documents related to current or future participation in the Plan by electronic means. You hereby consent to receive such documents by electronic delivery and agree to participate in the Plan through an on-line or electronic system established and maintained by Teradata or a third party designated by Teradata. If you have received this Agreement or any other document related to the Plan translated into a language other than English and if the translated version is different than the English version, the English version will control.

21. You hereby explicitly and unambiguously acknowledge and consent to the collection, use and transfer, in electronic or other form, of your Personal Data (as defined below) and any other Share Unit grant materials by and among, as applicable, Teradata, the Employer or third parties as may be selected by Teradata, for the exclusive purpose of implementing, administering and managing your participation in the Plan, enforcing the terms of and exercising their rights under this agreement to which it is a party and that relate directly or indirectly to you, and as necessary to comply with its obligations under Applicable Laws, rules and regulations with respect to your participation in the Plan. You further acknowledge and agree that such collection, storage, processing, use and transfer are for legitimate purposes and are necessary for the operation of the Plan. You understand that refusal or withdrawal of consent will affect your ability to participate in the Plan; without providing consent, you will not be able to participate in the Plan or realize benefits (if any) from the Share Units or any other awards under the Plan.

You understand and acknowledge that Teradata and the Employer or designated third parties may receive, hold, process and transfer certain personal information about you, including, but not limited to, your name, home address and telephone number, date of birth, social insurance number or other identification number, salary, nationality, job title, employment history, any Shares or directorships held in Teradata, details of all Share Units or any other entitlement to Shares awarded, canceled, exercised, vested, unvested or outstanding in your favor (“Personal Data”).

You understand that Personal Data may be transferred to any Subsidiary or affiliate or third parties assisting Teradata with the implementation, administration and management of the Plan, or to a successor in interest to the stock, assets or business of Teradata. You understand the recipients of the Data may be located in your country, in the United States, or elsewhere and that the recipients’ country (e.g., the United States) may have different data privacy laws and protections than your country. In particular, the Company may transfer Personal Data to the broker or stock plan administrator assisting with the Plan, to its legal counsel and tax and accounting advisor, and to the Employer and its payroll provider.

You should also refer to the Teradata Corporation Global Privacy Policy (which is available to you separately and may be updated from time to time) for more information regarding the collection, use, storage, and transfer of your Personal Data.

EXHIBIT A

TERADATA CORPORATION

MUTUAL AGREEMENT TO ARBITRATE ALL EMPLOYMENT RELATED CLAIMS

Teradata Corporation, including its divisions, subsidiaries and related companies (collectively, “Teradata”), believes most employment-related disputes are best resolved through open and honest communication and, when necessary, through the company’s Internal Dispute Resolution Policy (the “IDR Policy”), outlined in detail at CMP 706. If a dispute cannot be resolved informally, and given our desire to establish a speedy, impartial and cost-effective way to resolve disputes, the final stage of the IDR Policy provides the unresolved matter will be submitted to final and binding arbitration. This is Teradata’s and my mutual Arbitration Agreement (“Agreement”).

This Agreement to arbitrate includes every possible claim, dispute, or cause of action, in law or equity, arising out of or relating in any way to my employment with Teradata or the termination of my employment, to the maximum extent permitted by law, whether asserted during my employment with Teradata or after it has ended, including claims that I or my heirs, successors, administrators, and assigns may have against Teradata or against any of its current and former officers, directors, employees, representatives, contractors, owners, shareholders, or agents in their capacity as such, and all successors and assigns of any of them, or claims that Teradata may have against me (collectively, “Claims”).

Claims subject to this Agreement include, but are not limited to, claims pursuant to any federal, state or local law or statute including (without limitation) the Age Discrimination in Employment Act, Title VII of the Civil Rights Act of 1964, the Americans With Disabilities Act of 1990, the Family and Medical Leave Act, the Fair Labor Standards Act, the federal Equal Pay Act, the Worker Adjustment and Retraining Notification Act, the Uniform Service Employment and Reemployment Rights Act, the Genetic Information Nondiscrimination Act, the California Fair Employment and Housing Act, the California Labor Code, the California Equal Pay Act, and the California Family Rights Act, all as amended; Claims for wages, overtime, or other compensation due; Claims involving meal and rest breaks; Claims for benefits (except where an employee benefit plan specifies that its claim procedure shall culminate in an arbitration procedure different from this one); Claims for breach of contract or other promise (oral or written, express or implied); Claims for any form of illegal discrimination or harassment under state or federal law; Claims for wrongful termination or discharge (constructive or actual); Claims for violation of any public policy; Claims for improper, unfair, and/or retaliatory treatment or dismissal; and all tort Claims. Claims not covered by this Agreement are claims for workers’ compensation benefits, unemployment compensation benefits, claims governed by ERISA or other claims that, as a matter of law, the parties cannot agree to arbitrate. I understand that while I still have a right to file a charge with a state or federal agency, I will submit the final resolution of any Claim to an arbitrator instead of a court or jury. Teradata and I acknowledge that, by entering into this Agreement, we both waive the right to resolve any Claims through a trial by jury, in exchange for the benefits of a speedy and less expensive dispute resolution procedure.

Teradata and I agree that we will resolve our disputes on an individual basis only. Except for representative claims under California’s Private Attorneys General Act (“PAGA”), which cannot be waived under applicable law and which are therefore excluded from this Agreement, Teradata and I expressly intend and agree that: (a) class action and representative action procedures are hereby waived and shall not be asserted, nor will they apply, in any arbitration pursuant to this Agreement; (b) we will not assert class action or representative action claims in arbitration or otherwise; and (c) we shall submit only our own, individual Claims in arbitration, including but not limited to an individual Claim under PAGA. The arbitrator may not consolidate more than one

person’s Claims and may not otherwise preside over any form of a representative or class proceeding. This Agreement also prevents me from participating in a class action (existing or future) that is brought by any other party.

The arbitration shall be governed by the Federal Arbitration Act. The hearing will be conducted by the American Arbitration Association (the “AAA”) under the AAA’s then applicable employment arbitration rules (except as those rules are modified by this Agreement) and presided over by a sole arbitrator. The AAA rules are available online at https://www.adr.org/Rules. To file a claim, I will only be required to pay the equivalent of the fee to file a complaint in a court of local jurisdiction. Teradata will pay any remaining fees that are specific to arbitration, including the arbitrator’s fees and expenses. However, Teradata and I will each pay our own attorneys’ fees and our own standard litigation costs. If we cannot mutually agree on an arbitrator, the arbitrator will be selected according to the AAA’s rules and procedures. The arbitrator shall have the exclusive authority to rule on any challenge to his or her own jurisdiction or to the validity, enforceability, or formation of any portion of this Agreement to arbitrate.

The arbitration hearing will be held in or near the city where I worked with Teradata, or as otherwise mutually agreed to by me and Teradata. To prepare for the hearing, both Teradata and I have the right to take the sworn deposition statements of two individuals and, in addition, any expert witness expected to testify at the hearing. All documents to be used as exhibits and a list of all potential witnesses will be exchanged at least two weeks in advance of the hearing. No other discovery will be permitted unless the arbitrator finds there is a compelling need to do so and this need outweighs our desire for a quick and inexpensive resolution of the dispute. The arbitrator may consider and grant prehearing dispositive motions as he/she deems appropriate. The arbitrator will make a decision using the substantive law of the state where the claim arose or federal law where applicable. The arbitrator shall: (a) have the same full authority to order relief as would a court or a jury (including but not limited to an award of attorneys’ fees or costs under any applicable statute or written agreement); and (b) issue a written arbitration decision including the arbitrator’s essential findings and conclusions and a statement of the award. The arbitrator’s award may be entered and enforced by any court with jurisdiction.

This Agreement is not an employment contract and does not alter the terms of my at-will employment relationship with Teradata. Our mutual willingness to submit all disputes to arbitration is consideration for this Agreement. As additional consideration, I understand Teradata requires me to sign this Agreement as a condition of the compensation and benefits provided to me now and during my employment with Teradata.

This is the entire Agreement between Teradata and me relating to arbitration and supersedes any other written or oral agreement relating to arbitration, except for the IDR Policy which remains in full force and effect (however, in the event this Agreement and the IDR Policy conflict, this Agreement shall govern). This Agreement to arbitrate shall survive termination of my employment at Teradata. I have had a full opportunity to review this Agreement and I understand and agree to its terms. This Agreement can only be revoked or modified by a writing signed by both me and an officer of Teradata. If any portion of this Agreement is held to be void or unenforceable under any federal, state, or local law, the rest of the Agreement will remain in full force and effect.

TERADATA CORP /DE/ 8-K