Offer Letter to Join the Board of Directors of Arch Therapeutics, Inc. dated July 19, 2018, by and between Arch Therapeutics, Inc. and Punit Dhillon

Exhibit 10.4

July 19, 2018

Punit Dhillon

11220 Corte Belleza

San Diego, CA 92130

Dear Punit:

I am pleased to confirm our offer to you to serve as an independent member of the Board of Directors (the “Board”) of Arch Therapeutics, Inc. (the “Company”), effective on the later of (i) the date upon which the Company receives your written acceptance of this offer; and (ii) 4:00 PM July 19, 2018 (the “Effective Date”).

As compensation for serving on the Board, you shall be granted an option to purchase 200,000 shares of the Company’s common stock (the “Option”) pursuant to the Arch Therapeutics, Inc. 2013 Stock Incentive Plan. The Option shall vest in twelve equal monthly installments. The grant and the vesting commencement dates each shall be the Effective Date. The exercise price per share shall equal the closing fair market value of the Company’s common stock on the Effective Date. Furthermore, you shall be paid a Board fee of $50,000 per year, paid in quarterly installments and prorated from the Effective Date.

It is understood that your directorship may terminate at any time and for any reason without prior notice and without additional compensation to you. In addition, all of your granted Options shall immediately become fully vested in the event of a change in control transaction.

Please indicate your acceptance of this offer to serve as a director of the Company by signing, dating and returning this letter to the Company. Furthermore, by signing and dating this letter, you are providing your consent to act as a director of the Company and you are acknowledging that you not disqualified to act as a director under the Laws of the Commonwealth of Nevada.

We look forward to your joining the Board.