Exhibit 4.21

CDC-    A

AMENDMENT TO

WARRANT TO PURCHASE SHARES OF COMMON STOCK OF

AMEDICA CORPORATION

This Amendment to Warrant to Purchase Shares of Common Stock (this “Amendment”) dated as of December 23, 2013, is made by and between Amedica Corporation, a Delaware corporation (the “Company”), and the undersigned, TGP Securities, Inc. (the “Warrant Holder”), and it hereby amends that certain Warrant to Purchase Shares of Common Stock of the Company originally issued as of [August 30/September 19], 2013 (the “Existing Warrant”), in connection with the Company’s offering of up to 100 units wherein each unit consisted of 50,000 shares of the Company’s Series F Convertible Preferred Stock and one five year warrant to acquire 25,000 shares of the Company’s common stock exercisable at $1.00 per share.

NOW, THEREFORE, in consideration of the mutual promises contained herein, and the benefits to be derived by each party hereunder, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Company and Warrant Holder, intending to be legally bound, hereby agree to amend the Existing Warrant, as set forth below and hereby agree as follows:

AGREEMENT:

Section 1. Amendments to Section 4 - Adjustments to Shares and Stated Purchase Price. Section 4 of the Existing Warrant is hereby amended by inserting an additional paragraph immediately following Section 4(b) as follows:

“(c) If the Company at any time after the date hereof through the Warrant Expiration Date issues or sells any stock or other security (other than warrants or options to subscribe for or purchase shares of Common Stock or Preferred Stock granted to employees or consultants to the Company or securities (including warrants) issued by the Company in connection with the closing of an initial public offering of Common Stock, or any strategic collaboration, license, or other similar transaction) that is at any time and under any circumstances, directly or indirectly convertible into, exercisable or exchangeable for, or which otherwise entitles the holder thereof to acquire any shares of Common Stock or Preferred Stock (the “Convertible Securities”), for a consideration per share less than the Stated Purchase Price then in effect or for which the Convertible Securities have a conversion rate of less than the Stated Purchase Price then in effect, then the Stated Purchase Price in effect immediately prior to such issuance or sale will be reduced, concurrently with such issue, to the consideration per share received by the Company for such issuance or sale.”

Section 2. No Further Amendments. Except as expressly amended hereby, the Existing Warrant is in all respects ratified and confirmed and all the terms, conditions, and provisions thereof shall remain in full force and effect.

Section 3. Effect of Amendment. This Amendment shall form a part of the Existing Warrant for all purposes, and each party thereto and hereto shall be bound hereby. From and after the execution of this Amendment by the parties hereto, any reference to the Existing Warrant shall be deemed a reference to the Existing Warrant as amended hereby.

Section 4. Headings. The descriptive headings contained in this Amendment are included for convenience of reference only and shall not affect in any way the meaning or interpretation of this Amendment.

Section 5. Counterparts; Facsimiles. This Amendment may be executed in one or more counterparts, and by the different parties hereto in separate counterparts, each of which when executed shall be deemed to be an original but all of which taken together shall constitute one and the same agreement. A facsimile or other electronically transmitted signature on this Amendment is as valid as an original signature.

Section 6. Governing Law. This Amendment and the rights and duties of the parties hereto shall be governed by, and construed and enforced in accordance with, the laws of the State of Delaware.

IN WITNESS WHEREOF, the Company and Warrant Holder have caused this Amendment to Warrant to Purchase Shares of Common Stock of Amedica Corporation to be executed and delivered as of the date first written above by their respective officers thereunto duly authorized.