Exhibit 4.1

AMENDMENT NO. 1 TO RIGHTS AGREEMENT

     Amendment No. 1 to Rights Agreement (this “Amendment”), dated as of November 20, 2011, between Transatlantic Holdings, Inc., a Delaware corporation (the “Company”), and American Stock Transfer & Trust Company, LLC, a New York limited liability company, as Rights Agent (the “Rights Agent”), to the Rights Agreement, dated as of July 27, 2011, between the Company and the Rights Agent (the “Rights Agreement”); all capitalized terms not defined herein shall have the meanings ascribed to such terms in the Rights Agreement.

     WHEREAS, the Company proposes to enter into an Agreement and Plan of Merger among Alleghany Corporation, a Delaware corporation (“Alleghany”), Shoreline Merger Sub, LLC, a Delaware limited liability company and a wholly owned subsidiary of Alleghany (“Merger Sub”), and the Company (as amended, supplemented, modified or replaced from time to time, the “Merger Agreement”);

     WHEREAS, the Board of Directors of the Company has determined that the Merger Agreement and the terms and conditions set forth therein and the transactions contemplated thereby, including, without limitation, the Merger (as defined in the Merger Agreement), are advisable and are fair to and in the best interests of the Company and its stockholders;

     WHEREAS, the Board of Directors of the Company has determined, in connection with its consideration of the Merger Agreement, that it is necessary and desirable to amend the Rights Agreement as set forth herein;

     WHEREAS, subject to certain limited exceptions, Section 27 of the Rights Agreement provides that the Company may in its sole and absolute discretion from time to time supplement and amend the Rights Agreement without the approval of any holders of the Rights;

     WHEREAS, this Amendment is permitted by Section 27 of the Rights Agreement; and

     WHEREAS, pursuant to Section 27, the Company hereby directs that the Rights Agreement shall be amended as set forth in this Amendment.

     NOW THEREFORE, in consideration of the foregoing premises and mutual covenants and agreements set forth herein, and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Company and the Rights Agent hereby agree as follows:

     Section 1. Amendment to Section 1. Section 1 of the Rights Agreement is hereby amended and supplemented by adding subsection (uu) which shall read as follows:

“(uu) ”Merger Agreement” shall mean the Agreement and Plan of Merger, dated as of November 20, 2011, by and among Alleghany Corporation, a Delaware corporation (“Alleghany”), Shoreline Merger Sub, LLC, a Delaware limited liability company and wholly owned subsidiary of Alleghany (“Merger Sub”), and the Company (as such agreement is amended, supplemented, modified or replaced from time to time).”

     Section 2. Amendment to Section 7(a). Section 7(a) of the Rights Agreement is hereby amended by adding the following sentence to the end thereof:

“Notwithstanding anything to the contrary in this Agreement, immediately prior to the Effective Time (as defined in the Merger Agreement) this Agreement shall automatically terminate (without any further action of the parties hereto), all Rights established hereunder shall automatically expire and such time shall be deemed the Expiration Date for all purposes of this Agreement.”

     Section 3. Addition of New Section 35. The Rights Agreement is amended by adding a new Section 35 thereof which shall read as follows:

“Section 35. Exception For Merger Agreement. Notwithstanding any provision of this Agreement to the contrary, none of a Section 11(a)(ii) Event, a Section 13 Event, a Distribution Date nor a Shares Acquisition Date shall be deemed to have occurred, none of Alleghany, Merger Sub or any of their Affiliates or Associates shall be deemed to have become an Acquiring Person, and no holder of any Rights shall be entitled to exercise such Rights under, or be entitled to any rights pursuant to, any of Sections 3, 7, 11 or 13 of this Agreement, in any such case by reason of (a) the approval, execution or delivery of the Merger Agreement or any amendments thereof approved in advance by the Board of Directors of the Company or (b) the commencement or, prior to termination of the Merger Agreement, the consummation of any of the transactions contemplated by the Merger Agreement in accordance with their respective provisions, including without limitation, the Merger (as defined in the Merger Agreement).”

     Section 4. Effective Date; Certification. This Amendment shall be deemed effective as of the date first written above, as if executed on such date. The officer of the Company executing this Amendment hereby certifies to the Rights Agent that the amendment to the Rights Agreement set forth in this Amendment is in compliance with Section 27 of the Rights Agreement and the certification contained in this Section 4 shall constitute the certification required by Section 27 of the Rights Agreement.

     Section 5. Governing Law. This Amendment shall be deemed to be a contract made under the laws of the State of Delaware and for all purposes shall be governed by, and construed in accordance with, the laws of such State applicable to contracts made and to be performed entirely within such State.

     Section 6. Severability. The terms, provisions, covenants or restrictions of this Amendment shall be deemed severable and the invalidity or unenforceability of any term, provision, covenant or restriction shall not affect the validity or enforceability of the other term,

provision, covenant or restriction hereof. If any term, provision, covenant or restriction of this Amendment, or the application thereof to any person or any circumstance, is invalid or unenforceable, (a) a suitable and equitable term, provision, covenant or restriction shall be substituted therefor in order to carry out, so far as may be valid and enforceable, the intent and purpose of such invalid or unenforceable term, provision, covenant or restriction and (b) the remainder of this Amendment and the application of such term, provision, covenant or restriction to other Persons or circumstances shall not be affected by such invalidity or unenforceability, nor shall such invalidity or unenforceability affect the validity or enforceability of such term, provision, covenant or restriction, or the application thereof, in any other jurisdiction.

     Section 7. Notice. The Rights Agent and the Company hereby waive any notice requirement with respect to each other under the Rights Agreement, if any, pertaining to the matters covered by this Amendment.

     Section 8. No Other Effect. Except as expressly set forth herein, the Rights Agreement shall not by implication or otherwise be supplemented or amended by virtue of this Amendment, but shall remain in full force and effect, as amended hereby.

     Section 9. 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.

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

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