Exhibit 10.4

AMENDMENT NO. 1

TO

SECOND AMENDED AND RESTATED REGISTRATION RIGHTS AGREEMENT

This Amendment No. 1 to the Second Amended and Restated Registration Rights Agreement (this “Amendment”) is made and entered into effective June 17, 2023 (the “Amendment Effective Date”) between Arch Therapeutics, Inc., a Nevada corporation (the “Company”), and certain holders of the Company’s securities identified on the signature pages hereto (collectively, the “Consenting Holders”). Capitalized terms not defined herein shall have the same meaning as set forth in the Second Amended and Restated Registration Rights Agreement.

RECITALS:

WHEREAS, the Company and the Consenting Holders identified on the signature pages thereto entered into the Second Amended and Restated Registration Rights Agreement dated as of May 15, 2023 (the “Second A&R Registration Rights Agreement”);

WHEREAS, Section 7(c) of the Second A&R Registration Rights Agreement provides that any provision of the Second A&R Registration Rights Agreement may be amended with the written consent of the Company and the Holders of 51% or more of the then outstanding Registrable Securities;

WHEREAS, the Company and the Consenting Holders wish to amend the Second A&R Registration Rights Agreement in order to extend the date of the Filing Deadline; and

WHEREAS, the Consenting Holders collectively constitute 51% or more of the outstanding Registerable Securities.

NOW, THEREFORE, for due and adequate consideration, the receipt and adequacy of which are hereby acknowledged, the parties agree as follows:

1. The definition of Filing Deadline in Section 1 of the Second A&R Registration Rights Agreement shall be amended and restated as follows:

““Filing Deadline” means: (i) with respect to the Initial Registration Statement, the date that is 45 days following the First Closing; (ii) with respect to the Second Closing Registration Statement, the date that is 45 days following the Uplist Transaction; and; (iii) with respect to the Third Closing Registration Statement, the date that is 45 days following the Uplist Transaction; and (iv) with respect to any additional Registration Statements which may be required pursuant to Section 2(c), the earliest practical date on which the Company is permitted by SEC Guidance to file such additional Registration Statement related to the Registrable Securities.”

2. Except as modified by this Amendment, all other terms and conditions in the Second A&R Registration Rights Agreement shall remain in full force and effect and this Amendment shall be governed by all provisions thereof, including Section 7(h) regarding governing law. No reference to this Amendment need be made in any instrument or document making reference to the Second A&R Registration Rights Agreement; any reference to the Second A&R Registration Rights Agreement in any such instrument or document shall be deemed a reference to the Second A&R Registration Rights Agreement as amended hereby. The Second A&R Registration Rights Agreement as amended hereby shall be binding upon the parties thereto and their respective assigns and successors.

3. This Amendment may be executed in separate counterparts, each such counterpart being deemed to be an original instrument, and all such counterparts shall together constitute the same agreement.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed by their respective authorized signatories as of the date first indicated above.

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SIGNATURE PAGE FOR CONSENTING HOLDERS FOLLOWS]

[CONSENTING HOLDERS SIGNATURE PAGES TO AMENDMENT]

IN WITNESS WHEREOF, the undersigned have caused this Amendment to be duly executed by their respective authorized signatories as of the date first indicated above.