Exhibit 10.4

AMENDMENT NUMBER TWO TO AGREEMENT

This is the second amendment (“Amendment No. 2”) to the AMENDED AND RESTATED PATENT LICENSE AGREEMENT (the “License Agreement”), between The Board of Regents of The University of Texas System (“Board”) on behalf of The University of Texas Health Science Center at Houston (“UTHSC-H”) and PLx Pharma Inc., a Texas corporation with its principal place of business at 8285 El Rio, Suite 130, Houston, Texas 77054 (“PLx”), with an Effective Date of December 11, 2009. Board, UTHSC-H, and PLx may individually be referred to as Party or collectively as the Parties. All capitalized or bolded terms used in this Amendment No. 2 and not otherwise defined herein shall have the meanings assigned to those terms in the License Agreement.

WHEREAS, the parties entered into a the License Agreement, which such License Agreement was amended by the Amendment Number One To Agreement dated April 15, 2011; and,

The parties hereby desire to further amend the License Agreement;

Now, therefore, the parties do hereby agree as follows:

Section 4.6 shall be amended and restated in its entirety as follows:

4.6         Reasonable commercial diligence shall require that PLx:

a.         On or before September 8, 2012, submit an NDA for a Licensed Product; and;

b.         On or before September 8, 2013, Sell or offer for Sale a Licensed Product.

Except as expressly provided in this Amendment No. 2, all other terms, conditions and provisions of the License Agreement shall continue in full force and effect as provided therein.

(Signature Page Follows)

Amendment No. 2 to Patent License Agreement

The University of Texas System and PLx Pharma, Inc.

Amendment No. 2 to Patent License Agreement

The University of Texas System and PLx Pharma, Inc.