Exhibit 4.13

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 18, 2012, is made by and between Amedica Corporation, a Delaware corporation (the “Company”), and the undersigned,                     (the “Warrant Holder”), and it hereby amends that certain Warrant to Purchase Shares of Common Stock of the Company (the “Existing Warrant”) originally issued in connection with the Company’s issuance and sale of its Senior Secured Subordinated Convertible Promissory Notes during the period beginning March 4, 2011 and ending February 15, 2012 (referred to herein collectively as the “Convertible Notes” and each individually as a “Convertible Note”).

WHEREAS, the requisite holders of Convertible Notes voted, consented and agreed to amend the Convertible Notes such that all of the Convertible Notes would be automatically converted into shares of the Company’s Series F Convertible Preferred Stock, par value $0.01 per share (“Series F Preferred Stock”), immediately prior to the Company entering into a term loan ($18 million) and a new revolving credit facility (up to $3.5 million) (the “GE Credit Facility”) with General Electric Capital Corporation (“GECC”) and/or with one or more of GECC’s affiliates or designees and such other lenders as may be determined by GECC (or determined by one or more of GECC’s affiliates or designees) (referred to herein collectively as the “GE Lenders”).

WHEREAS, on December 17, 2012, the Company and the GE Lenders completed the closing of the GE Credit Facility and the outstanding Convertible Notes automatically were converted into shares of Series F Preferred Stock immediately prior to the Company entering into the GE Credit Facility.

WHEREAS, in connection with the Company’s issuance of shares of Series F Preferred Stock upon conversion of the Convertible Notes, the Company now offers to amend the Existing Warrant, subject to the approval of the Warrant Holder, to (a) extend the Warrant Expiration Date (as defined therein) by four (4) additional years and (b) reduce the Stated Purchase Price (as defined therein) from $2.00 per share of Common Stock to $1.00 per share.

WHEREAS, Section 11 of the Existing Warrant provides that it may be amended only with the consent of the holder of such Existing Warrant, and the Warrant Holder and the Company have executed and delivered this Amendment.

NOW, THEREFORE, in consideration of the foregoing premises, 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, Amedica 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 1.1 Amendments.

(a) The words “$2.00 per share” that appear in the second sentence of the first paragraph of the Existing Warrant are deleted, and the words “$1.00 per share” are inserted in place thereof.

(b) The words “third anniversary” that appear in the penultimate sentence of the first paragraph of the Existed Warrant are deleted, and the words “seventh anniversary” are inserted in place thereof.

Section 1.2 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 1.3 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 1.4 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 1.5 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 1.6 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.