Exhibit 10.18

January 5, 2007

Mr. Eugene B. Jones

Dear Gene:

The purpose of this letter agreement (the “Agreement”) is to confirm the terms regarding your separation of employment from Amedica Corporation, a Delaware corporation (the “Company”). As more fully set forth below, the Company desires to provide you with severance pay in exchange for certain agreements by you.

1. Separation of Employment. You acknowledge that, pursuant to your retirement, your employment with the Company will terminate effective Friday, January 5, 2007 (the “Separation Date”). You acknowledge that from and after the Separation Date, you shall have no authority and shall not represent yourself as an employee or agent of the Company. This Agreement shall become effective (the “Effective Date”) on the 8th day following your acceptance of it as provided below.

2. Severance Pay/Options. In exchange for the mutual covenants set forth in this Agreement,

(i) the Company is providing you with a lump sum payment of $95,566, less all applicable federal, state, local and other employment-related deductions; you acknowledge that such payment was advanced to you prior to December 31, 2006 and the execution of this Agreement, but you have agreed and do agree that should you not accept or rescind your acceptance of this agreement, as you may under the provisions set forth below, you thereafter shall immediately refund such payment to the Company at the conclusion of the time in which you may accept this Agreement (or on rejection should you reject it prior to such time) or, should you accept and later rescind, contemporaneously with your notice of rescission;

(ii) all stock options previously granted to you by the Company which are currently in effect (collectively, the “Existing Stock Options”) shall terminate and be of no further force or effect immediately upon the grant to you by the Company of a nonqualified stock option exercisable for up to 65,000 shares of the Company’s common stock (the “New Stock Option”). The New Stock Option shall expire not later than June 30, 2014, and shall have an exercise price per share equal to the fair market value of a share of the Company’s common stock on the date of grant. The grant to you of the New Stock Option is subject to the approval of the Company’s Board of Directors and unless and until the Board acts, the Existing Stock Options shall remain in full force and effect in accordance with their respective terms.

You acknowledge and agree that the Severance Pay provided in this Agreement are not otherwise due or owing to you under any Company employment agreement (oral or written) or Company policy or practice, and that this Severance Pay to be provided to you is not intended to, and shall not constitute, a severance plan, and shall confer no benefit on anyone other than the parties hereto. You further acknowledge that except for the specific financial consideration set forth in this Agreement, you are not and shall not in the future be entitled to any other compensation including, without limitation, wages, bonuses, vacation pay, holiday pay or any other form of compensation or benefit.

3. Unemployment Benefits. The Company agrees that it will not contest any claim for unemployment benefits by you with the State of Utah. The Company, of course, shall not be required to falsify any information.

4. Cooperation. You agree that both during and at any time after your employment, you shall cooperate fully with the Company in connection with any matter or event relating to your employment or events that occurred during your employment, including, without limitation, in the defense or prosecution of any claims or actions now in existence or which may be brought or threatened in the future against or on behalf of the Company, including any claims or actions against its affiliates and its and their officers and employees. Your cooperation in connection with such matters, actions and claims shall include, without limitation, being available, upon reasonable notice to meet with the Company regarding matters in which you have been involved, and any contract matters or audits; to prepare for, attend and participate in any proceeding (including, without limitation, depositions, consultation, discovery or trial); to provide affidavits; to assist with any audit, inspection, proceeding or other inquiry; and to act as a witness in connection with any litigation or other legal proceeding affecting the Company. You further agree that should you be contacted (directly or indirectly) by any person or entity (for example, by any party representing an individual or entity) adverse to the Company, you shall promptly notify me or Reyn Gallacher. You shall be reimbursed for any reasonable costs and expenses incurred in connection with providing such cooperation under this section.

5. Additional Covenants by You. You expressly acknowledge and agree to the following:

(i) that prior to the termination of your employment, you shall return to the Company all Company documents (and any copies thereof) and property, and that you will abide by any and all common law and/or statutory obligations relating to protection and nondisclosure of the Company’s trade secrets and/or confidential and proprietary documents and information;

(ii) that all information relating in any way to the negotiation of this Agreement, including the terms and amount of financial consideration provided for in this Agreement, shall be held confidential by you and shall not be publicized or disclosed to any person (other than an immediate family member, legal counsel or financial advisor, provided that any such individual to whom disclosure is made agrees to be bound by these confidentiality obligations), business entity or government agency (except as mandated by state or federal law);

2

(iii) that you will not make any statements that are professionally or personally disparaging about, or adverse to, the interests of the Company (and its officers, directors and managers) including, but not limited to, any statements that disparage any such person, product, service, finances, financial condition, capability or any other aspect of the business of the Company, and that you will not engage in any conduct which is intended to harm professionally or personally the reputation of the Company (and its officers, directors and managers);

(iv) that the breach of any of the foregoing covenants by you shall constitute a material breach of this Agreement and shall relieve the Company of any further obligations hereunder and, in addition to any other legal or equitable remedy available to the Company, shall entitle the Company to recover any Severance Pay already paid to you pursuant to Section 2 of this Agreement.

6. Release of Claims. You hereby agree and acknowledge that by signing this Agreement and accepting the Severance Pay to be provided to you, and other good and valuable consideration provided for in this Agreement, you, except as expressly provided below, are waiving and releasing your right to assert any form of legal claim against the Company^1/ whatsoever for any alleged action, inaction or circumstance existing or arising from the beginning of time through the Effective Date. Your waiver and release herein, except as expressly provided below, is intended to bar any form of legal claim, charge, complaint or any other form of action (jointly referred to as “Claims”) against the Company seeking any form of relief including, without limitation, equitable relief (whether declaratory, injunctive or otherwise), the recovery of any damages or any other form of monetary recovery whatsoever (including, without limitation, back pay, front pay, compensatory damages, emotional distress damages, punitive damages, attorneys fees and any other costs) against the Company, for any alleged action, inaction or circumstance existing or arising through the Effective Date.

Without limiting the foregoing general waiver and release, you, except as expressly provided below, specifically waive and release the Company from any Claim arising from or related to your employment relationship with the Company or the termination thereof, including, without limitation:

3

You explicitly acknowledge that because you are over forty (40) years of age, you have specific rights under the Older Workers Benefits Protection Act (“OWBPA”), which prohibits discrimination on the basis of age, and that the releases set forth in this section are intended to release any right that you may have to file a claim against the Company alleging discrimination on the basis of age.

Notwithstanding the foregoing, this section does not:

4

Your waiver and release, however, are intended to be a complete bar to any recovery or personal benefit by or to you with respect to any claim whatsoever, including those raised through a charge with the EEOC, except those which, as a matter of law, cannot be released. In the event that you successfully challenge the validity of the release with respect to the Age Discrimination in Employment Act, the Company or any affected party sought to be released hereunder may seek recovery from you of all amounts paid pursuant to this Agreement. Nothing in this Agreement, however, shall limit the right of the Company or any affected party sought to be released hereunder to seek immediate dismissal of a charge on the basis that your signing of this Agreement constitutes a full release of any rights you might otherwise have to pursue the charge.

You acknowledge and agree that, but for providing this waiver and release, you would not be receiving the Severance Pay being provided to you under the terms of this Agreement.

It is the Company’s desire and intent to make certain that you fully understand the provisions and effects of this Agreement. To that end, you have been encouraged and given the opportunity to consult with legal counsel for the purpose of reviewing the terms of this Agreement. Consistent with the provisions of OWBPA, the Company is providing you with twenty-one (21) days in which to consider and accept the terms of this Agreement by signing below and returning it to Ashok Khandkar, Amedica Corporation, 615 Arapeen Drive, Suite 302, Salt Lake City, UT 84108. In addition, you must rescind your assent to this Agreement within seven (7) days after you sign it. To do so, you must deliver a notice of rescission to Ashok Khandkar. To be effective, such rescission must be hand delivered or postmarked within the seven (7) day period and sent by certified mail, return receipt requested, to Ashok Khandkar, Amedica Corporation, 615 Arapeen Drive, Suite 302, Salt Lake City, UT 84108,

7. Entire Agreement/Modification/Waiver/Choice of Law/Enforceability/Jury Waiver. You acknowledge and agree that, with the exception of your Confidentiality and Assignment of Inventions Agreement, your so called “lock-up” agreement dated May 26, 2006, the Amended and Restated Registration Rights Agreement among the Company and certain of its securityholders, any restrictive covenants relating to your employment, this Agreement supersedes any and all prior or contemporaneous oral and/or written agreements between you and the Company, and sets forth the entire agreement between you and the Company. No variations or modifications hereof shall be deemed valid unless reduced to writing and signed by the parties hereto. The failure of the Company to seek enforcement of any provision of this Agreement in any instance or for any period of time shall not be construed as a waiver of such provision or the Company’s right to seek enforcement of such provision in the future. This Agreement shall be deemed to have been made in the State of Utah, shall take effect as an instrument under seal within Utah, and shall be governed by and construed in accordance with the laws of the State of Utah, without giving effect to conflict of law principles. You agree that any action, demand, claim or counterclaim relating to the terms and provisions of this Agreement, or to its formation

5

or breach, shall be commenced in Salt Lake City, Utah in a court of competent jurisdiction, and you further acknowledge that venue for such actions shall lie exclusively in Utah and that material witnesses and documents would be located in Utah. Both parties hereby waive and renounce in advance any right to a trial by jury in connection with such legal action. The provisions of this Agreement are severable, and if for any reason any part hereof shall be found to be unenforceable, the remaining provisions shall be enforced in full.

By executing this Agreement, you are acknowledging that you have been afforded sufficient time to understand the terms and effects of this Agreement, that your agreements and obligations hereunder are made voluntarily, knowingly and without duress, and that neither the Company nor its agents or representatives have made any representations inconsistent with the provisions of this Agreement.

This Agreement may be signed on one or more copies, each of which when signed will be deemed to be an original, and all of which together will constitute one and the same Agreement.

If the foregoing correctly sets forth our understanding, please sign, date and return the enclosed copy of this Agreement to me at the Company within twenty-one (21) days.

Dated: January 5, 2007

6