EXHIBIT 10.4

Private Units Purchase AGREEMENT

This Private Units Purchase Agreement (this “Agreement”) is made as of , 2025, by and between Aimei Health Technology II Co., Ltd., a Cayman Islands exempted company (the “Company”), having its principal place of business at 10 East 53rd Street, Suite 3001, New York, NY 10022, and Aimei investment II Ltd, a Cayman Islands exempted company (the “Purchaser”).

WHEREAS, the Company desires to sell on a private placement basis (the “Offering”) an aggregate of up to 285,234 units (the “Initial Units”) of the Company, and up to an additional 13,500 Units (“Additional Units” and together with the Initial Units, the “Units”) of the Company in the event that the underwriters’ 45-day over-allotment option (“Over-Allotment Option”) in the Offering is exercised in full or part, each Unit comprised of one Class A ordinary share, par value $0.0001 per share (“Ordinary Shares”) and one right to receive one-seventh (1/7 of one Ordinary Share upon the consummation of an initial business combination (the “Rights.

WHEREAS, the Purchaser desires to purchase the 285,234 Initial Units and up to 13,500 Additional Units and the Company wishes to accept such subscription.

NOW, THEREFORE, in consideration of the promises and the mutual covenants hereinafter set forth and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Company and the Purchaser hereby agree as follows:

1. Agreement to Subscribe

1.1 Purchase and Issuance of the Units. For the aggregate sum of $2,852,340 (the “Initial Purchase Price”), upon the terms and subject to the conditions of this Agreement, the Purchaser hereby agrees to purchase from the Company, and the Company hereby agrees to sell to the Purchaser, on the Closing Date (as defined in Section 1.2) 285,234 Initial Units at $10.00 per Initial Unit.

In addition to the foregoing, the Purchaser hereby agrees to purchase up to an additional 13,500 Additional Units at $10.00 per Additional Unit for a purchase price of up to $135,000 (the “Additional Purchase Price” and together with the Initial Purchase Price, the “Purchase Price”). The purchase and issuance of the Additional Units shall occur only in the event that the Over-Allotment Option is exercised in full or part. The total number of Additional Units to be purchased hereunder shall be in the same proportion as the amount of the Over-Allotment Option that is exercised. Each purchase of Additional Units shall occur simultaneously with the consummation of any portion of the Over-Allotment Option.

1.2 Closing. The closing of the purchase and sale of the Initial Units shall take place at the offices of Rimon, P.C. simultaneously with the consummation of the Company’s initial public offering (“IPO”) of 6,000,000 units consisting of Ordinary Shares and Rights and the purchase and sale of the Additional Units shall take place upon the consummation of the exercise of all or any portion of the Over-Allotment Option (each a “Closing Date”).

1.3 Delivery of the Purchase Price. The Initial Purchase Price is currently held in an account at [ ] (“[ ]”). At least one business day prior to the effective date of the Company’s two registration statements relating to the IPO (collectively “Registration Statement”), or the date of the exercise of the Over-Allotment Option, if any, the Purchaser agrees to deliver the Initial Purchase Price or Additional Purchase Price, as the case may be, by certified bank check or wire transfer of immediately available funds denominated in United States Dollars to [ ], which is hereby irrevocably authorized to deposit such funds on the applicable Closing Date to the trust account which will be established for the benefit of the Company’s public shareholders, managed pursuant to that certain Investment Management Trust Agreement to be entered into by and between the Company and [ ] and into which substantially all of the proceeds of the IPO will be deposited (the “Trust Account”). If the IPO is not consummated within 14 days of the date the Initial Purchase Price is delivered to [ ], the Initial Purchase Price shall be returned to the Purchaser by certified bank check or wire transfer of immediately available funds denominated in United States Dollars, without interest or deduction.

1.4 Delivery of Unit Certificate. Upon the applicable Closing Date after delivery of the Purchase Price in accordance with Section 1.3, the Purchaser shall become irrevocably entitled to receive a unit certificate representing the Units purchased hereunder.

2. Representations and Warranties of the Purchaser

The Purchaser represents and warrants to the Company that:

2.1 No Government Recommendation or Approval. It understands that no United States federal or state agency or similar agency of any other country has passed upon or made any recommendation or endorsement of the Company, the Offering, the Units, the Rights or the Ordinary Shares underlying the Units (collectively, the “Securities”).

2.2 Organization. It is a business company, validly existing and in good standing under the laws of the Cayman Islands and possesses all requisite power and authority necessary to carry out the transactions contemplated by this Agreement.

2.3 Private Offering. It is an “accredited investor” as such term is defined in Rule 501(a) of Regulation D under the Securities Act of 1933, as amended (the “Securities Act”) or it is not a “U.S. Person” as defined in Rule 902 of Regulation S (“Regulation S”) under the Securities Act. It acknowledges that the sale contemplated hereby is being made in reliance on a private placement exemption to “Accredited Investors” within the meaning of Section 501(a) of Regulation D under the Securities Act and similar exemptions under state law or a non-U.S. Person under Regulation S.

2.4 Authority. This Agreement has been validly authorized, executed and delivered by the Purchaser and is a valid and binding agreement enforceable in accordance with its terms, except as such enforceability may be limited by applicable bankruptcy, insolvency, fraudulent conveyance or similar laws affecting the enforcement of creditors’ rights generally and subject to general principles of equity (regardless of whether enforcement is sought in a proceeding at law or in equity).

2.5 No Conflicts. The execution, delivery and performance of this Agreement and the consummation by the Purchaser of the transactions contemplated hereby do not violate, conflict with or constitute a default under (i) the Purchaser’s organizational documents, (ii) any agreement, indenture or instrument to which the Purchaser is a party or (iii) any law, statute, rule or regulation to which the Purchaser is subject, or any agreement, order, judgment or decree to which the Purchaser is subject.

2.6 No Legal Advice from Company. It acknowledges it has had the opportunity to review this Agreement and the transactions contemplated by this Agreement and the other agreements entered into between the parties hereto with its own legal counsel and investment and tax advisors. Except for any statements or representations of the Company made in this Agreement and the other agreements entered into between the parties hereto, it is relying solely on such counsel and advisors and not on any statements or representations of the Company or any of its representatives or agents for legal, tax or investment advice with respect to this investment, the transactions contemplated by this Agreement or the securities laws of any jurisdiction.

2.7 Access to Information; Independent Investigation. Prior to the execution of this Agreement, it has had the opportunity to ask questions of and receive answers from representatives of the Company concerning an investment in the Company, as well as the finances, operations, business and prospects of the Company, and the opportunity to obtain additional information to verify the accuracy of all information so obtained. In determining whether to make this investment, it has relied solely on its own knowledge and understanding of the Company and its business based upon its own due diligence investigation and the information furnished pursuant to this paragraph. It understands that no person has been authorized to give any information or to make any representations which were not furnished pursuant to this Section 2 and it has not relied on any other representations or information in making its investment decision, whether written or oral, relating to the Company, its operations and/or its prospects.

2.8 Reliance on Representations and Warranties. It understands the Units are being offered and sold to it in reliance on exemptions from the registration requirements under the Securities Act, and analogous provisions in the laws and regulations of various states, and that the Company is relying upon the truth and accuracy of the representations, warranties, agreements, acknowledgments and understandings of the Purchaser set forth in this Agreement in order to determine the applicability of such provisions.

2.9 No Advertisements. It is not subscribing for the Units as a result of or subsequent to any advertisement, article, notice or other communication published in any newspaper, magazine, or similar media or broadcast over television or radio, or presented at any seminar or meeting.

2.10 Legend. It acknowledges and agrees the certificates evidencing the Units, the Shares and the Rights shall bear a restrictive legend (the “Legend”), in form and substance as set forth in Section 4 hereof, prohibiting the offer, sale, pledge or transfer of the securities, except (i) pursuant to an effective registration statement covering these securities under the Securities Act or (ii) pursuant to any other exemptions from the registration requirements under the Securities Act and such laws which, in the opinion of counsel for the Company, is available.

2.11 Experience, Financial Capability and Suitability. It is (i) sophisticated in financial matters and is able to evaluate the risks and benefits of the investment in the Securities and (ii) able to bear the economic risk of his investment in the Securities for an indefinite period of time because the Securities have not been registered under the Securities Act and therefore cannot be sold unless subsequently registered under the Securities Act or an exemption from such registration is available. It has substantial experience in evaluating and investing in transactions of securities in companies similar to the Company so that it is capable of evaluating the merits and risks of its investment in the Company and has the capacity to protect its own interests. It has substantial experience in evaluating and investing in transactions of securities in companies similar to the Company so that it is capable of evaluating the merits and risks of its investment in the Company and has the capacity to protect its own interests.

2.12 Investment Purposes. It is purchasing the Securities solely for investment purposes, for its own account and not for the account or benefit of any other person, and not with a view towards the distribution or dissemination thereof and it has no present arrangement to sell the interest in the Securities to or through any person or entity.

2.13 Restrictions on Transfer. It acknowledges and understands the Units are being offered in a transaction not involving a public offering in the United States within the meaning of the Securities Act. The Securities have not been registered under the Securities Act, and, if in the future, it decides to offer, resell, pledge or otherwise transfer the Securities, such Securities may be offered, resold, pledged or otherwise transferred only (A) pursuant to an effective registration statement filed under the Securities Act, (B) pursuant to an exemption from registration under Rule 144 promulgated under the Securities Act (“Rule 144”), if available, or (C) pursuant to any other available exemption from the registration requirements of the Securities Act, and in each case in accordance with any applicable securities laws of any state or any other jurisdiction. It agrees that if any transfer of its Securities or any interest therein is proposed to be made, as a condition precedent to any such transfer, it may be required to deliver to the Company an opinion of counsel satisfactory to the Company. Absent registration or another available exemption from registration, it agrees it will not resell the Securities. It further acknowledges that because the Company is a shell company, Rule 144 may not be available to it for the resale of the Securities until the one year anniversary following consummation of the initial Business Combination (defined below) of the Company, despite technical compliance with the requirements of Rule 144 and the release or waiver of any contractual transfer restrictions.

3. Representations and Warranties of the Company

The Company represents and warrants to the Purchaser that:

3.1 Valid Issuance of Share Capital. The total number of all classes of share capital which the Company has authority to issue is 60,000,000 Ordinary Shares , 6,000,000 Class B ordinary shares of par value $0.0001 each and 600,000 preference shares of par value $0.0001 each. As of the date hereof, 1,725,000 Class B ordinary shares of the Company are issued and outstanding, and the Company has not issued any Ordinary Shares or preference shares. All of the issued share capital of the Company has been duly authorized, validly issued, and are fully paid and non-assessable.

3.2 Title to Securities. Upon issuance in accordance with the terms hereof, the rights agreement to be entered into with ☑ on or prior to the closing of the IPO (“Rights Agreement”) and the Amended and Restated Memorandum and Articles of Association of the Company, as the case may be, each of the Rights and the Ordinary Shares will be duly and validly issued, fully paid and non-assessable. On the date of issuance of the Units, the Rights and Ordinary Shares shall have been reserved for issuance. Upon issuance in accordance with the terms hereof, the Rights Agreement and the Amended and Restated Memorandum and Articles of Association of the Company, the Purchaser will have or receive good title to the Units, Rights and Ordinary Shares, free and clear of all liens, claims and encumbrances of any kind.

3.3 Organization and Qualification. The Company has been duly incorporated and is validly existing as a Cayman Islands exempted company and has the requisite corporate power to own its properties and assets and to carry on its business as now being conducted.

3.4 Authorization; Enforcement. (i) The Company has the requisite corporate power and authority to enter into and perform its obligations under this Agreement and to issue the Securities in accordance with the terms hereof, (ii) the execution, delivery and performance of this Agreement by the Company and the consummation by it of the transactions contemplated hereby have been duly authorized by all necessary corporate action, and (iii) this Agreement constitutes, and upon the execution and delivery thereof, the Rights and the Rights Agreement will constitute, valid and binding obligations of the Company enforceable against the Company in accordance with their respective terms, except as such enforceability may be limited by applicable bankruptcy, insolvency, fraudulent conveyance, moratorium, reorganization, or similar laws relating to, or affecting generally the enforcement of, creditors’ rights and remedies or by equitable principles of general application and except as enforcement of rights to indemnity and contribution may be limited by federal and state securities laws or principles of public policy.

3.5 No Conflicts. The execution, delivery and performance of this Agreement and the consummation by the Company of the transactions contemplated hereby do not (i) result in a violation of the Company’s Memorandum and Articles of Association, (ii) conflict with, or constitute a default under any agreement, indenture or instrument to which the Company is a party or (iii) conflict with any law statute, rule or regulation to which the Company is subject or any agreement, order, judgment or decree to which the Company is subject. Other than any federal, state or foreign securities filings which may be required to be made by the Company subsequent to the Closing, and any registration statement which may be filed pursuant thereto, the Company is not required under federal, state or local law, rule or regulation to obtain any consent, authorization or order of, or make any filing or registration with, any court or governmental agency or self-regulatory entity in order for it to perform any of its obligations under this Agreement or issue the Units, the Rights or the Ordinary Shares underlying the Units in accordance with the terms hereof.

4. Legends

4.1 Legend. The Company will issue the Units, the Rights and the Ordinary Shares purchased by the Purchaser, in the name of the Purchaser. The Securities will bear the following Legend and appropriate “stop transfer” instructions:

THESE SECURITIES (i) HAVE NOT BEEN REGISTERED UNDER THE UNITED STATES SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), AND THESE SECURITIES MAY NOT BE OFFERED, SOLD, PLEDGED OR OTHERWISE TRANSFERRED EXCEPT (A) PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT FILED UNDER THE SECURITIES ACT, (B) TO A NON-U.S. PERSON IN AN OFFSHORE TRANSACTION IN ACCORDANCE WITH RULE 903 OR RULE 904 OF REGULATION S UNDER THE SECURITIES ACT, (C) PURSUANT TO THE RESALE LIMITATIONS SET FORTH IN RULE 905 OF REGULATION S UNDER THE SECURITIES ACT, (D) PURSUANT TO AN EXEMPTION FROM REGISTRATION PROVIDED BY RULE 144 UNDER THE SECURITIES ACT (IF AVAILABLE) OR (E) PURSUANT TO ANY OTHER EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT, IN EACH CASE IN ACCORDANCE WITH ANY APPLICABLE SECURITIES LAWS OF ANY STATE OF THE UNITED STATES OR ANY OTHER JURISDICTION. HEDGING TRANSACTIONS INVOLVING THESE SECURITIES MAY NOT BE CONDUCTED UNLESS IN COMPLIANCE WITH THE SECURITIES ACT.

“THE SECURITIES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO AN AGREEMENT BETWEEN AIMEI HEALTH TECHNOLOGY II CO., LTD AND AIMEI INVESTMENT II LTD. AND MAY ONLY BE OFFERED, SOLD, TRANSFERRED, PLEDGED OR OTHERWISE DISPOSED DURING THE TERM OF THE LOCKUP PURSUANT TO THE TERMS SET FORTH THEREIN.”

4.2 Purchaser’s Compliance. Nothing in this Section 4 shall affect in any way the Purchaser’s obligations and agreements to comply with all applicable securities laws upon resale of the Securities.

4.3 Company’s Refusal to Register Transfer of the Securities. The Company shall refuse to register any transfer of the Securities, if in the sole judgment of the Company such purported transfer would not be made (i) pursuant to an effective registration statement filed under the Securities Act, or (ii) pursuant to an available exemption from the registration requirements of the Securities Act.

4.4 Registration Rights. The Purchaser will be entitled to certain registration rights which will be governed by a registration rights agreement (“Registration Rights Agreement”) to be entered into with the Company on or prior to the closing of the IPO.

5. Lockup

The Purchaser acknowledges and agrees that the Units, the Rights and Ordinary Shares shall not be transferable, saleable or assignable until the consummation of an acquisition, share exchange, purchase of all or substantially all of the assets of, or any other similar business combination with one or more businesses or entities (a “Business Combination”), except to permitted transferees (as defined in the Insider Letter).

6. Securities Laws Restrictions

The Purchaser agrees not to sell, transfer, pledge, hypothecate or otherwise dispose of all or any part of the Securities unless, prior thereto (a) a registration statement on the appropriate form under the Securities Act and applicable state securities laws with respect to the Securities proposed to be transferred shall then be effective or (b) the Company shall have received an opinion from counsel reasonably satisfactory to the Company, that such registration is not required because such transaction complies with the Securities Act and the rules promulgated by the Securities and Exchange Commission thereunder and with all applicable state securities laws.

7. Waiver of Distributions from Trust Account

In connection with the Securities purchased pursuant to this Agreement, the Purchaser hereby waives any and all right, title, interest or claim of any kind in or to any distributions from the Trust Account.

8. Rescission Right Waiver and Indemnification

8.1 Rescission Waiver. The Purchaser understands and acknowledges that an exemption from the registration requirements of the Securities Act requires there be no general solicitation of purchasers of the Units. In this regard, if the Offering were deemed to be a general solicitation with respect to the Units, the offer and sale of such Units may not be exempt from registration and, if not, the Purchaser may have a right to rescind its purchase of the Units. In order to facilitate the completion of the Offering and in order to protect the Company, its shareholders and the Trust Account from claims that may adversely affect the Company or the interests of its shareholders, the Purchaser hereby agrees to waive, to the maximum extent permitted by applicable law, any claims, right to sue or rights in law or arbitration, as the case may be, to seek rescission of its purchase of the Units as a result of the issuance of the Units being deemed to be in violation of Section 5 of the Securities Act. The Purchaser acknowledges and agrees this waiver is being made in order to induce the Company to sell the Units to the Purchaser. The Purchaser agrees the foregoing waiver of rescission rights shall apply to any and all known or unknown actions, causes of action, suits, claims or proceedings (collectively, “Claims”) and related losses, costs, penalties, fees, liabilities and damages, whether compensatory, consequential or exemplary, and expenses in connection therewith, including reasonable attorneys’ and expert witness fees and disbursements and all other expenses reasonably incurred in investigating, preparing or defending against any Claims, whether pending or threatened, in connection with any present or future actual or asserted right to rescind the purchase of the Units hereunder or relating to the purchase of the Units and the transactions contemplated hereby.

8.2 No Recourse Against Trust Account. The Purchaser agrees not to seek recourse against the Trust Account for any reason whatsoever in connection with its purchase of the Units or any Claim that may arise now or in the future.

8.3 Section 8 Waiver. The Purchaser agrees that to the extent any waiver of rights under this Section 8 is ineffective as a matter of law, the Purchaser has offered such waiver for the benefit of the Company as an equitable right that shall survive any statutory disqualification or bar that applies to a legal right. The Purchaser acknowledges the receipt and sufficiency of consideration received from the Company hereunder in this regard.

9. Terms of the Unit

The Units shall be substantially identical to the Units offered in the IPO as set forth in the Underwriting Agreement, except the Units: (i) will be subject to the transfer restrictions described herein, and (ii) are being purchased pursuant to an exemption from the registration requirements of the Securities Act and will become freely tradable only after certain conditions are met or the resale of the Units is registered under the Securities Act.

10. Governing Law; Jurisdiction; Waiver of Jury Trial

This Agreement shall be governed by and construed in accordance with the laws of the State of New York for agreements made and to be wholly performed within such territory. The parties hereto hereby waive any right to a jury trial in connection with any litigation pursuant to this Agreement and the transactions contemplated hereby.

11. Assignment; Entire Agreement; Amendment

11.1 Assignment. Neither this Agreement nor any rights hereunder may be assigned by any party to any other person other than by the Purchaser, without the prior consent of the Company, to one or more persons agreeing to be bound by the terms hereof. Upon such assignment by a Purchaser, the assignee(s) shall become Purchaser hereunder and have the rights and obligations provided for herein to the extent of such assignment.

11.2 Entire Agreement. This Agreement sets forth the entire agreement and understanding between the parties as to the subject matter hereof and supersedes any and all prior discussions, agreements and understandings of any and every nature.

11.3 Amendment. Except as expressly provided in this Agreement, neither this Agreement nor any term hereof may be amended, waived, discharged or terminated other than by a written instrument signed by the party against whom enforcement of any such amendment, waiver, discharge or termination is sought.

11.4 Binding upon Successors. This Agreement shall be binding upon and inure to the benefit of the parties hereto and to their respective heirs, legal representatives, successors and permitted assigns.

12. Notices; Indemnity

12.1 Notices. All notices, requests, consents and other communications hereunder shall be in writing, shall be addressed to the receiving party’s address set forth herein or to such other address as a party may designate by notice hereunder, and shall be either (a) delivered by hand, (b) sent by overnight courier, or (c) sent by certified mail, return receipt requested, postage prepaid. All notices, requests, consents and other communications hereunder shall be deemed to have been given either (i) if by hand, at the time of the delivery thereof to the receiving party at the address of such party set forth above, (ii) if sent by overnight courier, on the next business day following the day such notice is delivered to the courier service, or (iii) if sent by certified mail, on the seventh business day following the day such mailing is made.

12.2 Indemnification. Except as set forth in Section 8, each party shall indemnify the other party against any loss, cost or damages (including reasonable attorney’s fees and expenses) incurred as a result of such party’s breach of any representation, warranty, covenant or agreement set forth in this Agreement.

13. Counterparts

This Agreement may be executed in one or more counterparts, all of which when taken together shall be considered one and the same agreement and shall become effective when counterparts have been signed by each party and delivered to the other party, it being understood that both parties need not sign the same counterpart. In the event that any signature is delivered by facsimile transmission or any other form of electronic delivery, such signature shall create a valid and binding obligation of the party executing (or on whose behalf such signature is executed) with the same force and effect as if such signature page were an original thereof.

14. Survival; Severability

14.1 Survival. The representations, warranties, covenants and agreements of the parties hereto shall survive the Closing until one (1) year following the consummation of an initial Business Combination.

14.2 Severability. In the event that any provision of this Agreement becomes or is declared by a court of competent jurisdiction to be illegal, unenforceable or void, this Agreement shall continue in full force and effect without said provision; provided that no such severability shall be effective if it materially changes the economic benefit of this Agreement to any party.

15. Headings

The titles and subtitles used in this Agreement are used for convenience only and are not to be considered in construing or interpreting this Agreement.

16. Construction

The parties hereto have participated jointly in the negotiation and drafting of this Agreement. If an ambiguity or question of intent or interpretation arises, this Agreement will be construed as if drafted jointly by the parties hereto and no presumption or burden of proof will arise favoring or disfavoring any party hereto because of the authorship of any provision of this Agreement. The words “include,” “includes,” and “including” will be deemed to be followed by “without limitation.” Pronouns in masculine, feminine, and neuter genders will be construed to include any other gender, and words in the singular form will be construed to include the plural and vice versa, unless the context otherwise requires. The words “this Agreement,” “herein,” “hereof,” “hereby,” “hereunder,” and words of similar import refer to this Agreement as a whole and not to any particular subdivision unless expressly so limited. The parties hereto intend that each representation, warranty, and covenant contained herein will have independent significance. If any party hereto has breached any representation, warranty, or covenant contained herein in any respect, the fact that there exists another representation, warranty or covenant relating to the same subject matter (regardless of the relative levels of specificity) which such party hereto has not breached will not detract from or mitigate the fact that such party hereto is in breach of the first representation, warranty, or covenant.

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This subscription is accepted by the Company as of the date first written above.

By:
Name:
Title:

Accepted and agreed this

, 2025

AIMEI INVESTMENT II LTD

By:
Name:
Title:

[Signature Page for Unit Subscription Agreement]

Aimei Health Technology II Co., Ltd. S-1