FIRST AMENDMENT TO THE AMENDED AND RESTATED TAX BENEFIT PRESERVATION PLAN

Exhibit 4.1

FIRST AMENDMENT TO THE

AMENDED AND RESTATED TAX BENEFIT PRESERVATION PLAN

This First Amendment to the Amended and Restated Tax Benefit Preservation Plan (this “Amendment”) dated as of May 3, 2010, is entered into between Radian Group Inc., a Delaware corporation (the “Company”), and The Bank of New York Mellon, a New York banking corporation, as Rights Agent (the “Rights Agent”).

Background

A. The Company and Rights Agent are parties to that certain Amended and Restated Tax Benefit Preservation Plan, dated as of February 12, 2010 (the “Preservation Plan”).

B. The Company wishes to amend the Preservation Plan to add a termination provision if the Preservation Plan is not re-approved by the stockholders of the Company every three years.

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

1. Amendment. The Preservation Plan shall be amended by inserting a new provision (Section 7(f)) that reads in its entirety as follows:

In addition to the provision set forth in Section 7(a) of this Plan, the Expiration Date shall occur on the Close of Business on the second Business Day after the final adjournment of the third consecutive annual meeting of the stockholders of the Company held after this Plan was most recently approved by the stockholders of the Company unless the Plan is re-approved by the stockholders at such meeting.

2. 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.

3. Severability. If any term, provision, covenant or restriction of this Amendment or applicable to this Amendment is held by a court of competent jurisdiction or other authority to be invalid, null and 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; and provided, further, that if any such excluded term, provision, covenant or restriction shall adversely affect the rights, immunities, duties or obligations of the Rights Agent, the Rights Agent shall be entitled to resign immediately.

4. 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 to be made and performed entirely within such State.

5. Descriptive Headings. Descriptive headings of the several sections of this Amendment are inserted for convenience only and shall not control or affect the meaning or construction of any of the provisions hereof.

6. Defined Terms. All capitalized terms used herein and not otherwise defined shall have the meaning given to them in the Preservation Plan.

7. Preservation Plan in Full Force and Effect as Amended. Except as specifically amended hereby, all of the terms and conditions of the Preservation Plan shall be in full force and effect. All references to the Preservation Plan in any other document or instrument shall be deemed to mean such Preservation Plan as amended by this Amendment. The parties hereto agree to be bound by the terms and obligations of the Preservation Plan, as amended by this Amendment, as though the terms and obligations of the Preservation Plan were set forth herein.

[Signatures of the parties intentionally appear on the next page.]

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed as of the 3rd day of May, 2010.