3.1

CERTIFICATE OF AMENDMENT

OF THE

THIRD AMENDED AND RESTATED

CERTIFICATE OF INCORPORATION

OF

TRANSGENOMIC, INC.

Pursuant to Sections 211 and 242 of the

General Corporation Law of the

State of Delaware

TRANSGENOMIC, INC., a corporation organized and existing under and by virtue of the General Corporation Law of the State of Delaware (the “DGCL”);

DOES HEREBY CERTIFY THAT:

FIRST: The name of the Corporation is TRANSGENOMIC, INC. (the “Corporation”).

SECOND: The Third Amended and Restated Certificate of Incorporation of the Corporation was filed with the office of the Secretary of State of the State of Delaware on October 26, 2005 (the “Restated Certificate”).

THIRD: Article IV, Section 4.1 of the Restated Certificate is hereby deleted in its entirety and replaced by the following new Article IV, Section 4:

“Section 4.1. The total number of shares of capital stock which the Corporation shall have authority to issue is 165,000,000 consisting of (a) 150,000,000 shares of Common Stock, par value $0.01 per share, and (b) 15,000,000 shares of Preferred Stock, par value $0.01 per share.”

FOURTH: The foregoing amendment has been duly adopted by the Board of Directors of the Corporation acting in accordance with the provisions of Section 242 of the DGCL, and further adopted in accordance with the provisions of Sections 211 and 242 of the DGCL by the stockholders of the Corporation.

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IN WITNESS WHEREOF, this Certificate of Amendment of the Third Amended and Restated Certificate of Incorporation has been duly executed by the undersigned officer of the Corporation this 23rd day of May, 2012.