FIRST AMENDMENT TO CHANGE IN CONTROL SEVERANCE AGREEMENT

Exhibit 10.4

FIRST AMENDMENT TO CHANGE IN CONTROL SEVERANCE AGREEMENT

THIS FIRST AMENDMENT TO CHANGE IN CONTROL SEVERANCE AGREEMENT (this “Amendment”) is made and entered into this 13th day of October, 2015 by and between Cempra, Inc., a Delaware corporation with its principal executive offices at 6320 Quadrangle Drive, Suite 360, Chapel Hill, NC 27517 (the “Company”), and Mark W. Hahn (the “Employee”).

WITNESSETH:

WHEREAS, Employee and the Company previously entered into a Change in Control Severance Agreement (the “Severance Agreement”) as of May 23, 2014;

WHEREAS, Employee and the Company wish to amend the Severance Agreement to alter certain provisions regarding the consideration to be paid to Employee under certain circumstances following a “Change in Control” of the Company;

WHEREAS, the Company wishes to protect its investment in its business, employees, customer relationships, and confidential information, by requiring Employee to abide by certain restrictive covenants regarding competition and other matters, each of which is an inducement to the Company to provide Employee with the benefits described in this Amendment; and

WHEREAS, in light of the foregoing, Employee and the Company desire to mutually and voluntarily amend the Severance Agreement, effective as of the date set forth above (the “Effective Date”), pursuant to the terms set forth herein.

NOW, THEREFORE, in consideration of the foregoing, the mutual promises herein contained, and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto, intending to be legally bound, agree as follows.

1. AMENDMENT TO SECTION 1(d) OF THE SEVERANCE AGREEMENT. Section 1 of the Severance Agreement is modified by replacing existing Section 1(d)(v) with a new Section 1(d)(v) as follows:

(v) The determination by the Company, after a reasonable and good-faith investigation by the Company following a written allegation by another employee of the Company, that Employee personally engaged in some form of discrimination, harassment or retaliatory conduct prohibited by law (including, without limitation, discrimination based on race, color, religion, sex, national origin, age, disability or other status protected by law);

2. AMENDMENT TO SECTION 1(f) OF THE SEVERANCE AGREEMENT. Section 1 of the Severance Agreement is modified by replacing existing Section 1(f) with a new Section 1(f) as follows:

(f) “Good Reason” shall mean any of the following: (i) the assignment to Employee of duties materially inconsistent with Employee’s position, duties, responsibilities, titles or offices as described herein; (ii) material reduction by the Company of Employee’s duties and responsibilities; (iii) any reduction or series of reductions in excess of ten percent (10%) by the Company of Employee’s compensation or benefits payable hereunder (it being understood that a reduction of benefits applicable to all employees of the Company, including Employee, shall not be deemed a reduction of Employee’s compensation package for purposes of this definition); or (iv) a change of more than thirty-five (35) miles in the geographic location at which Employee must perform services for the Company. Notwithstanding the foregoing, Employee shall not have Good Reason for termination unless Employee gives written notice of termination for Good Reason within thirty (30) days after the event giving rise to Good Reason occurs, and the Company does not correct the action or failure to act that constitutes the grounds for Good Reason, as set forth in Employee’s notice of termination, within thirty (30) days after the date on which Employee gives written notice of termination.

3. AMENDMENT TO SECTION 2 OF THE SEVERANCE AGREEMENT. Section 2 of the Severance Agreement is modified by replacing existing Section 2(b) with a new Section 2(b) as follows:

(b) In addition, if during the Term of this Agreement, Employee’s employment with the Company is terminated within twelve (12) months after a Change in Control, either by the Company without Cause (and other than due to death or Disability) or by Employee for Good Reason, and (1) such termination results in Employee incurring a “separation from service” as defined under Treasury Regulation 1.409A-1(h); (2) Employee has not breached this Agreement, or the Confidentiality and Assignment of Inventions Agreement; and (3) conditioned upon Employee’s execution of an Effective Release, Employee shall be entitled to, in lieu of any other separation payment or severance benefit:

(i) Payment of an amount equal to twelve (12) months of his Base Salary, minus applicable withholdings required by law or authorized by Employee, to be paid pursuant to the Company’s standard payroll practices and procedures, beginning on the Company’s next regular pay day occurring sixty (60) days following the Termination Date (the “Termination Compensation”);

(ii) Payment in a lump sum, on the Company’s next regular pay day occurring sixty (60) days following the Termination Date, of a pro rata bonus based upon Employee’s target bonus amount for the year in which the Termination Date occurs, pro-rated for the portion of the calendar year through the Termination Date;

(iii) Accelerated vesting of all outstanding and unvested stock options and other equity in the Company held by Employee, which shall become immediately and fully exercisable, subject to all other terms of the applicable equity plan and award agreement; and

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(iv) Conditioned on Employee’s proper and timely election to continue his health insurance benefits under COBRA after the Termination Date, reimbursement of Employee’s applicable COBRA premiums for the lesser of twelve (12) months following the Termination Date or until Employee becomes eligible for insurance benefits from another employer, provided, however, that the Company has the right to terminate such payment of COBRA premium reimbursement to Employee and instead pay Employee a lump sum amount equal to the applicable COBRA premium multiplied by the number of months remaining in the specified period if the Company determines in its discretion that continued payment of the COBRA premiums is or may be discriminatory under Section 105(h) of the Internal Revenue Code.

4. ADDITION OF SECTION 7 TO THE SEVERANCE AGREEMENT. The Severance Agreement is further amended by adding a new Section 7 as follows:

7. Non-Competition, Non-Solicitation and Non-Disparagement.

(a) While Employee is employed by the Company and for a period of twelve (12) months after the termination or cessation of such employment by either party for any reason whatsoever, Employee will not, directly on Employee’s own behalf or indirectly for or in conjunction with others:

(i) Within the Restricted Territory (as defined in subsection (b) below), engage in any business or enterprise (whether as owner, partner, officer, director, employee, consultant, investor, lender or otherwise) that develops, manufactures, markets, licenses or sells any pharmaceutical antibiotic products that compete with the products being sold or developed by the Company at the time of Employee’s termination (collectively, the “Competitive Products”) in any management or executive role in which Employee would perform duties that are the same or substantially similar to those duties actually performed by Employee for the Company in the twelve (12) months immediately prior to the termination of Employee’s employment, or in any position where Employee or such business or enterprise would benefit from Employee’s use or disclosure of the Company’s Proprietary Information as defined in the Confidentiality and Assignment of Inventions Agreement;

(ii) Within the Restricted Territory, solicit or accept employment or be retained by an individual or entity who, at any time during the term of this Agreement, was an agent, client, licensee, or customer of the Company, where Employee would have any management or executive role or be in any position (whether as an employee, contractor or consultant) in which Employee would perform duties that are the same or substantially similar to those duties actually performed by Employee for the Company in the twelve (12)

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months immediately prior to the termination of Employee’s employment or in any position where Employee or such individual or entity would benefit from Employee’s use or disclosure of the Company’s Proprietary Information as defined in the Confidentiality and Assignment of Inventions Agreement;

(iii) Within the Restricted Territory, become financially interested in an enterprise that is engaged, as a substantial part of its operations, in developing, manufacturing, marketing, licensing or selling the Competitive Products; provided, however, that nothing in this Agreement shall be construed to prevent Employee from owning less than five percent (5%) of the outstanding voting securities of any entity whose voting securities are listed on a national securities exchange;

(iv) Solicit or accept the business of any customer of the Company whom Employee solicited or serviced for the Company during the last twelve (12) months of Employee’s employment with the Company for the purpose of selling or providing Competitive Products to such customer; and/or

(v) Solicit, induce or encourage any employee, consultant, or independent contractor of the Company to terminate his or her employment or contracting relationship with the Company.

(b) For purposes of this Agreement, the “Restricted Territory” means North America; but if such territory is determined to be overly broad, then the United States; and, if such territory is also determined to be overly broad, then each state or province in North America in which the Company engages in material business activities or sells or licenses its products. Provided, however, that it shall not be a violation of this Section 7 for Employee to work outside of the Restricted Territory for any business or enterprise that develops, manufactures, markets, licenses or sells Competitive Products, so long as that business or enterprise does not manufacture, market, license or sell any Competitive Products that compete with the Company’s products within the Restricted Territory.

(c) During Employee’s employment with the Company and at all times thereafter, the Company and Employee each further agree that neither party shall directly or indirectly disparage or defame the name or reputation of the other party or any of its affiliates, including but not limited to any officer, director, employee or shareholder of the Company or any of its affiliates.

(d) In the event of a breach or threatened breach of this Section 7 by Employee, then, in addition to any other rights which the Company may have, (i) the Company will have the right to immediately terminate any remaining payment obligations to Employee pursuant to Section 2(b)(i), 2(b)(ii), and 2(b)(iv) above without any further obligation to Employee, and Employee will immediately repay to the Company any amounts previously paid to Employee pursuant to

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Section 2(b)(i), 2(b)(ii), and 2(b)(iv) above; (ii) the Company will be entitled to injunctive relief to enforce this Section 7 (and notwithstanding anything set forth in Section 6(b) above, the Company may seek injunctive relief in any court of competent jurisdiction without waiving the right to arbitration under Section 6(b)); and (iii) the Company will have the right to require Employee to account for and pay over to the Company all compensation, profits, monies, accruals, increments and other benefits (collectively, the “Benefits”) derived or received by Employee as a result of any transaction constituting a breach of any of the provisions of Section 7, and Employee hereby agrees to account for and pay over such Benefits to the Company. Notwithstanding the foregoing, the sole remedy available to the Company with respect to a breach by Employee of (a)(i), (a)(iii) or (a)(iv) above that relates to Competitive Products other than a product or products in the fusidane or macrolide classes of products shall be termination effective as of the breach of any remaining payment obligations pursuant to Section 2(b) of this Agreement.

(e) Each of the rights and remedies enumerated in Section 7(d) shall be independent of the others and shall be in addition to, and not in lieu of, any other rights and remedies available to the Company at law or in equity. If any of the covenants contained in this Section 7, or any part of any of them, is hereafter construed or adjudicated to be invalid or unenforceable, the same shall not affect the remainder of the covenant or covenants or rights or remedies which shall be given full effect without regard to the invalid portions. If any of the covenants contained in this Section 7 is held to be invalid or unenforceable because of the duration of such provision or the area covered thereby, the parties agree that the court or arbitrator making such determination shall have the power to reduce the duration and/or area of such provision and in its reduced form such provision shall then be enforceable. No such holding of invalidity or unenforceability in one jurisdiction shall bar or in any way affect the Company’s right to the relief provided in this Section 7 or otherwise in the courts of any other state or jurisdiction within the geographical scope of such covenants as to breaches of such covenants in such other respective states or jurisdictions, such covenants being, for this purpose, severable into diverse and independent covenants.

(f) The provisions of this Section 7 will survive any termination of this Agreement and the termination of Employee’s employment with the Company.

5. CONSIDERATION FOR COVENANT NOT TO COMPETE. Employee acknowledges that one of the effects of this Amendment is to make a post-employment covenant not to compete a part of the Severance Agreement. Employee acknowledges and agrees that such covenant not to compete is supported by adequate consideration, including, but not limited to, the Company’s agreement to provide enhanced benefits pursuant to the amended Section 2(b) of the Severance Agreement. The Company would not have agreed to amend Section 2(b) of the Severance Agreement but for Employee’s agreement to the restrictions imposed by new Section 7 of the Severance Agreement.

6. REMAINDER OF SEVERANCE AGREEMENT. Except as expressly set forth in this Amendment, the provisions of the Severance Agreement will remain in full force and effect, in their entirety, in accordance with their terms.

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7. MISCELLANEOUS. This Amendment will be governed, construed, and interpreted in accordance with the laws of the State of North Carolina, without giving effect to conflicts of laws principles of any jurisdiction. The parties agree that this Amendment may only be modified in a signed writing executed by each of the parties hereto. This Amendment will be binding upon and will inure to the benefit of the parties hereto and their respective heirs, successors and assigns. This Amendment may be executed in separate counterparts, each of which is deemed to be an original and all of which taken together constitute one agreement. Facsimile or PDF reproductions of original signatures will be deemed binding for the purpose of the execution of this Amendment.

IN WITNESS WHEREOF, the parties hereto have executed this Amendment to be effective as of the Effective Date.

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