FIRST AMENDMENT TO CREDIT AGREEMENT

Exhibit 10.4

FIRST AMENDMENT TO CREDIT AGREEMENT

THIS FIRST AMENDMENT TO CREDIT AGREEMENT (this “First Amendment”) is made and entered into as of the 15^th day of December, 2005, by and among

(i) RADIAN GROUP INC., a Delaware corporation, and its successors and assigns (the “Borrower”);

(ii) THE FINANCIAL INSTITUTIONS as signatory lender parties hereto and their successors and assigns (collectively, the “Lenders”, with each individually a “Lender”); and

(iii) KEYBANK NATIONAL ASSOCIATION, a national banking association, in its capacity as Administrative Agent for the Lenders under this Agreement, and its successors and assigns (the “Administrative Agent”).

Recitals:

A. The Borrower, the Lenders, the Administrative Agent and certain other parties are the parties to that certain Credit Agreement dated as of December 16, 2004 (the “Credit Agreement”), pursuant to which, inter alia, the Lenders agreed, subject to the terms and conditions thereof, to advance Loans (as this and other capitalized terms used herein and not otherwise defined herein are defined in the Credit Agreement) to the Borrower.

B. The Borrower has requested that the Lenders agree to amend the Credit Agreement to extend the 364-Day Revolving Availability Termination Date.

C. Subject to the terms and conditions of this First Amendment, the Lenders have agreed to grant such request.

Agreements:

NOW, THEREFORE, in consideration of the foregoing Recitals and the mutual agreements hereinafter set forth, the Borrower, the Lenders and the Administrative Agent, intending to be legally bound, hereby agree as follows:

1. Amendment to Credit Agreement. The definition of 364-Day Revolving Availability Termination Date in Section 1.01 (Defined Terms) of the Credit Agreement is hereby amended and restated in its entirety to provide as follows:

“364-Day Revolving Availability Termination Date” means December 14, 2006 (or if such date is not a Business Day with respect to Eurodollar Loans, the next preceding day that is a Business Day with respect to Eurodollar Loans).

2. Amendment Effective Date; Conditions Precedent. The amendment set forth in Paragraph 1, above, shall not be effective unless and until the date on which the Borrower has satisfied all of the following conditions precedent (such date of effectiveness being the “Amendment Effective Date”):

A. Officer’s Certificate. On the Amendment Effective Date and after giving effect to the amendment set forth in Paragraph 1, above, (i) there shall exist no Default, and a Senior Officer of the Borrower shall have delivered to the Administrative Agent written confirmation thereof dated as of the Amendment Effective Date, and (ii) the representations and warranties of the Borrower under Article 3 of the Credit Agreement shall have been reaffirmed in writing as being true and correct in all material respects as of the Amendment Effective Date, except that for the purposes of such reaffirmation references in such representations and warranties to (a) the “Effective Date” shall be deemed to refer to the Amendment Effective Date, (b) “December 31, 2003” shall be deemed to refer to December 31, 2004, (c) “September 30, 2004” shall be deemed to refer to September 30, 2005 and (d) Schedule 3.06 to the Credit Agreement shall be

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deemed to refer to the revised Schedule 3.06 attached to such reaffirmation, which revised Schedule 3.06 shall be satisfactory in form and substance to the Administrative Agent in its reasonable discretion.

B. Corporate Authorization. The Borrower shall have delivered to the Administrative Agent a copy, certified by its Secretary or Assistant Secretary, of its Board of Directors’ resolutions authorizing the execution and delivery of this First Amendment.

C. Legal Matters. All legal matters incident to this First Amendment and the consummation of the transactions contemplated hereby shall be reasonably satisfactory to Squire, Sanders & Dempsey L.L.P., Cleveland, Ohio, special counsel to the Administrative Agent and the Lenders (the “Special Counsel”).

D. Other Matters. The Administrative Agent and the Lenders shall have received such other certificates, opinions and documents, in form and substance reasonably satisfactory to the Administrative Agent, as the Administrative Agent may reasonably request.

3. Other Loan Documents. Any reference to the Credit Agreement in the other Loan Documents shall, from and after the Amendment Effective Date, be deemed to refer to the Credit Agreement, as amended by this First Amendment.

4. Confirmation of Agreement. The Borrower hereby affirms all of its obligations to the Lenders and the Administrative Agent under the Credit Agreement and the other Loan Documents and that as of the Amendment Effective Date the Borrower has no claims, defenses or set-offs to the obligations of the Borrower to each of them under the Credit Agreement and the other Loan Documents.

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5. Administrative Agent’s Expense. The Borrower agrees to reimburse the Administrative Agent promptly for its reasonable documented out-of-pocket costs and expenses incurred in connection with this First Amendment and the transactions contemplated hereby, including, without limitation, the reasonable fees and expenses of the Special Counsel.

6. No Other Modifications. Except as expressly provided in this First Amendment, all of the terms and conditions of the Credit Agreement and the other Loan Documents remain unchanged and in full force and effect.

7. Governing Law; Binding Effect. This First Amendment shall be governed by and construed in accordance with the laws of the State of New York and shall be binding upon and inure to the benefit of the Borrower, the Lenders and the Administrative Agent and their respective successors and assigns.

8. Counterparts. This First Amendment may be executed in separate counterparts, each of which shall be deemed to be an original, and all of which together shall be deemed a fully executed agreement.

IN WITNESS WHEREOF, the Borrower, the Lenders and the Administrative Agent have hereunto set their hands as of the date first above written.

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