Exhibit 4.1

EXECUTION VERSION

FIRST AMENDMENT TO THE RIGHTS AGREEMENT

BETWEEN

J. ALEXANDER’S CORPORATION

AND

COMPUTERSHARE TRUST COMPANY, N.A.

THIS FIRST AMENDMENT TO THE RIGHTS AGREEMENT (this “Amendment”) is made as of June 22, 2012, between J. Alexander’s Corporation, a Tennessee corporation (the “Company”), and Computershare Trust Company, N.A., a federally chartered trust company (the “Rights Agent”). Capitalized terms used but not otherwise defined in this Amendment shall have the meanings given them in the Rights Agreement.

WHEREAS, the Company and the Rights Agent are parties to that certain Rights Agreement, dated as of March 5, 2012 (the “Rights Agreement”);

WHEREAS, the Company is contemplating entering into an Agreement and Plan of Merger (as the same may be amended from time to time, the “Merger Agreement”), by and among the Company, Fidelity National Financial, Inc., a Delaware corporation (“Parent”), Fidelity Newport Holdings, LLC, a Delaware limited liability company (“Operating Company”), American Blue Ribbon Holdings, Inc., a Delaware corporation and an indirect, majority-owned subsidiary of Parent (“Purchaser”), and Athena Merger Sub, Inc., a Tennessee corporation and direct, wholly owned subsidiary of Purchaser (“Merger Sub”), pursuant to which Merger Sub will be merged with and into the Company with the Company as the surviving corporation thereof (the “Merger”);

WHEREAS, the Board of Directors of the Company has approved the Merger Agreement and the Merger and determined that an amendment to the Rights Agreement as set forth herein is desirable in connection with the execution and delivery of the Merger Agreement, and the Company and the Rights Agent desire to evidence such amendment in writing;

WHEREAS, upon the execution and delivery of the Merger Agreement, Parent, Operating Company, Purchaser, Merger Sub and/or their Associates and Affiliates may be deemed to be Acquiring Persons under the Rights Agreement, which would trigger certain events pursuant to the terms of the Rights Agreement; and

WHEREAS, pursuant to Section 27 of the Rights Agreement, the Board of Directors of the Company has approved this Amendment and authorized its appropriate officers to execute and deliver the same to the Rights Agent.

NOW, THEREFORE, in consideration of the promises and agreements set forth herein, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

1. Amendment of Section 1(a): Definition of “Acquiring Person.” The definition of “Acquiring Person” set forth in Section 1(a) of the Rights Agreement is hereby amended by adding the following sentence to the end of that definition:

“Notwithstanding anything in this Agreement to the contrary, no Person shall become an Acquiring Person by reason of (i) the execution and delivery of the Merger Agreement (or any amendment thereto), or of any agreement or document contemplated by the Merger Agreement or in furtherance of the transactions contemplated thereby, or the public announcement of any of the foregoing, or (ii) the consummation of the transactions contemplated thereby, including the Merger.”

2. Amendment of Section 1(h): Definition of “Distribution Date.” The definition of “Distribution Date” set forth in Section 1(h) of the Rights Agreement is hereby deleted and restated in its entirety as follows:

“‘Distribution Date’ shall have the meaning set forth in Section 3(a) hereof; provided, however, that, notwithstanding anything in this Agreement to the contrary, a Distribution Date shall not be deemed to have occurred by reason of (i) the execution and delivery of the Merger Agreement (or any amendment thereto), or of any agreement or document contemplated by the Merger Agreement or in furtherance of the transactions contemplated thereby, or the public announcement of any of the foregoing, or (ii) the consummation of the transactions contemplated thereby, including the Merger.”

3. Amendment of Section 1(z): Definition of “Shares Acquisition Date.” The definition of “Shares Acquisition Date” set forth in Section 1(z) of the Rights Agreement is hereby amended by adding the following sentence to the end of that definition:

“Notwithstanding anything in this Agreement to the contrary, a Shares Acquisition Date shall not be deemed to have occurred by reason of (i) the execution and delivery of the Merger Agreement (or any amendment thereto), or of any agreement or document contemplated by the Merger Agreement or in furtherance of the transactions contemplated thereby, or the public announcement of any of the foregoing, or (ii) the consummation of the transactions contemplated thereby, including the Merger.”

4. Amendment of Section 1: Other Definitions. Section 1 of the Rights Agreement is hereby further amended by adding the following subparagraphs at the end thereof:

(ee) “Amendment” shall mean the First Amendment to the Rights Agreement, dated as of June 22, 2012, between the Company and the Rights Agent.

(ff) “Merger” shall have the meaning set forth in Section 35 hereof.

(gg) “Merger Agreement” shall have the meaning set forth in Section 35 hereof.

(hh) “Merger Sub” shall have the meaning set forth in Section 35 hereof.

(ii) “Operating Company” shall have the meaning set forth in Section 35 hereof.

(jj) “Parent” shall have the meaning set forth in Section 35 hereof.

(kk) “Purchaser” shall have the meaning set forth in Section 35 hereof.

5. Amendment of Section 11(a)(ii). Section 11(a)(ii) of the Rights Agreement is hereby amended by adding the following sentence to the end thereof:

“Notwithstanding anything in this Agreement to the contrary, neither (i) the execution and delivery of the Merger Agreement (or any amendment thereto), or of any agreement or document contemplated by the Merger Agreement or in furtherance of the transactions contemplated thereby, or the public announcement of any of the foregoing, nor (ii) the consummation of the transactions contemplated thereby, including the Merger, shall be deemed to be an event described in this Section 11(a)(ii) or cause the Rights to be adjusted or to become exercisable in accordance with this Section 11 or otherwise.”

6. Amendment of Section 13. Section 13 of the Rights Agreement is hereby amended by adding the following sentence to the end thereof:

“Notwithstanding anything in this Agreement to the contrary, neither the execution and delivery of the Merger Agreement (or any amendment thereto), or of any agreement or document contemplated by the Merger Agreement or in furtherance of the transactions contemplated thereby, or the public announcement of any of the foregoing, nor (ii) the consummation of the transactions contemplated thereby, including the Merger, shall be deemed to be an event described in this Section 13 or cause the Rights to be adjusted or to become exercisable in accordance with this Section 13 or otherwise.”

7. Amendment of Section 25. Section 25 of the Rights Agreement is hereby amended by adding the following sentence to the end thereof:

“Notwithstanding anything in this Agreement to the contrary, neither the execution and delivery of the Merger Agreement (or any amendment thereto), or of any agreement or document contemplated by the Merger Agreement or in furtherance of the transactions contemplated thereby, or the public announcement of any of the foregoing, nor (ii) the consummation of the transactions contemplated thereby, including the Merger, shall be deemed to be an event requiring any notice described in this Section 25.”

8. Addition of Section 35. The Rights Agreement is hereby further modified, supplemented and amended in by adding the following new Section 35:

“Section 35. Merger with [Merger Sub]. The Company, Fidelity National Financial, Inc., a Delaware corporation (“Parent”), Fidelity Newport Holdings, LLC, a Delaware limited liability company (“Operating Company”), American Blue Ribbon Holdings, Inc., a Delaware corporation and an indirect, majority-owned subsidiary of Parent (“Purchaser”), and Athena Merger Sub, Inc., a Tennessee corporation and direct, wholly owned subsidiary of Purchaser (“Merger Sub”), have entered into an Agreement and Plan of Merger, dated as of June 22, 2012, (as it may be amended from time to time, the “Merger Agreement”) pursuant to which the Company agrees, among other things, to merge with Merger Sub, with the Company being the surviving entity and a wholly owned subsidiary of Parent following the consummation of the merger, according to the terms and conditions set forth in the Merger Agreement (the “Merger”). Notwithstanding anything in this Agreement to the contrary, if the Merger Agreement shall be terminated for any reason, then all of the amendments to this Agreement effected by the Amendment shall be deemed repealed and deleted without any further action on the part of the Company or the Rights Agent, and the Company will promptly notify the Rights Agent of such repeal and deletion.”

9. Effectiveness. This Amendment shall be deemed effective as of, and immediately prior to, the execution and delivery of the Merger Agreement, and the Company will promptly notify the Rights Agent of effective date of this Amendment. The Rights Agreement, as amended by this Amendment, shall remain in full force and effect in accordance with its terms and shall be otherwise unaffected hereby.

10. Successors. All the covenants and provisions of this Amendment by or for the benefit of the Company or the Rights Agent shall bind and inure to the benefit of their respective successors or assigns hereunder.

11. Benefits of this Amendment. Nothing in this Amendment shall be construed to give to any Person other than the Company, the Rights Agent and the registered holders of the Right Certificates (and, prior to the Distribution Date, the associated Common Shares) any legal or equitable right, remedy or claim under this Amendment or the Rights; but this Amendment shall be for the sole and exclusive benefit of the Company, the Rights Agent and the registered holders of the Rights (and, prior to the Distribution Date, the associated Common Shares).

12. Severability. The invalidity or unenforceability of any term or provision hereof shall not affect the validity or enforceability of any other term or provision hereof. If any term, provision, covenant or restriction of this Amendment is held by a court of competent jurisdiction or other authority to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Amendment shall remain in full force and effect and shall in no way be affected, impaired or invalidated.

13. Governing Law. This Amendment shall be deemed to be a contract made under the laws of the State of Tennessee and for all purposes shall be governed by and construed in accordance with the laws of said State applicable to contracts to be made and performed entirely within said State, except that the rights, duties, and obligations of the Rights Agent shall be governed by, and construed in accordance with, the laws of the Commonwealth of Massachusetts applicable to contracts to be made and performed entirely within such state.

14. Counterparts. This Amendment may be executed in any number of counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument. A signature to this Amendment transmitted electronically shall have the same authority, effect, and enforceability as an original signature.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed and attested, all as of the day and year first above written.