EXHIBIT 4.4 FORM OF EXCHANGE GLOBAL NOTE

EXHIBIT 4.4

FORM OF EXCHANGE GLOBAL NOTE

UNLESS THIS CERTIFICATE IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF THE DEPOSITORY TRUST COMPANY, A NEW YORK CORPORATION (“DTC”), TO THE ISSUER OR ITS AGENT FOR REGISTRATION OF TRANSFER, EXCHANGE OR PAYMENT AND ANY CERTIFICATE ISSUED IS REGISTERED IN THE NAME OF CEDE & CO. OR IN SUCH OTHER NAME AS IS REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC AND ANY PAYMENT IS MADE TO CEDE & CO. OR TO SUCH OTHER ENTITY AS IS REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC, ANY TRANSFER, PLEDGE, OR OTHER USE HEREOF FOR VALUE OR OTHERWISE BY OR TO ANY PERSON IS WRONGFUL INASMUCH AS THE REGISTERED OWNER HEREOF, CEDE & CO., HAS AN INTEREST HEREIN.

UNLESS AND UNTIL THIS CERTIFICATE IS EXCHANGED IN WHOLE OR IN PART FOR NOTES IN CERTIFICATED FORM, THIS CERTIFICATE MAY NOT BE TRANSFERRED EXCEPT AS A WHOLE BY DTC TO A NOMINEE THEREOF OR BY A NOMINEE THEREOF TO DTC OR ANOTHER NOMINEE OF DTC OR BY DTC OR ANY SUCH NOMINEE TO A SUCCESSOR OF DTC OR A NOMINEE OF SUCH SUCCESSOR.

CUSIP/CINS: 885218 AB 3                        

8.00% Senior Notes due 2013

THORNBURG MORTGAGE, INC.

promises to pay to Cede & Co., or registered assigns, the principal sum of Fifty Five Million Dollars on May 15, 2013.

Interest Payment Dates: May 15 and November 15

Record Dates: May 1 and November 1

Dated:                         , 2004

SEAL

This is one of the Notes referred to

in the within-mentioned Supplemental Indenture:

[Back of Note]

8.00% Senior Notes due 2013

Capitalized terms used herein shall have the meanings assigned to them in the First Supplemental Indenture referred to below unless otherwise indicated.

1. INTEREST. Thornburg Mortgage, Inc., a Maryland corporation (the “Company”), promises to pay interest on the principal amount of this Note at 8.00% per annum from November 15, 2003 until maturity. The Company will pay interest semi-annually in arrears on May 15 and November 15 of each year, or if any such day is not a Business Day, on the next succeeding Business Day (each an “Interest Payment Date”). Interest on this Note will accrue from the most recent date to which interest has been paid or, if no interest has been paid, from November 15, 2003; provided that if there is no existing Default in the payment of interest, and if this Note is authenticated between a record date referred to on the face hereof and the next succeeding Interest Payment Date, interest shall accrue from such next succeeding Interest Payment Date; provided, further, that the first Interest Payment Date shall be May 15, 2004. The Company shall pay interest (including post-petition interest in any proceeding under any Bankruptcy Law) on overdue principal and premium, if any, from time to time on demand at the rate then in effect; it shall pay interest (including post-petition interest in any proceeding under any Bankruptcy Law) on overdue installments of interest (without regard to any applicable grace periods) from time to time on demand at the same rate to the extent lawful. Interest will be computed on the basis of a 360-day year of twelve 30-day months.

2. METHOD OF PAYMENT. The Company will pay interest on the Notes (except defaulted interest) to the Persons who are registered Holders of Notes at the close of business on the May 1 or November 1 next preceding the Interest Payment Date, even if such Notes are canceled after such record date and on or before such Interest Payment Date, except as provided in Section 2.14 of the First Supplemental Indenture with respect to defaulted interest. The Notes will be payable as to principal, premium, if any, and interest at the office or agency of the Company maintained for such purpose within or without the City and State of New York, or, at the option of the Company, payment of interest may be made by check mailed to the Holders at their addresses set forth in the register of Holders, and provided that payment by wire transfer of immediately available funds will be required with respect to principal of and interest, and premium, if any, on, all Global Notes and all other Notes the Holders of which shall have provided wire transfer instructions to the Company or the Paying Agent. Such payment shall be in such coin or currency of the United States of America as at the time of payment is legal tender for payment of public and private debts. The Company reserves the right to pay interest to Holders of Notes by check mailed to such Holders at their registered addresses or by wire transfer to Holders of at least $5 million aggregate principal amount of Notes.

3. PAYING AGENT AND REGISTRAR. Initially, Deutsche Bank Trust Company Americas, the Trustee under the First Supplemental Indenture, will act as Paying Agent and Registrar. The Company may change any Paying Agent or Registrar without notice to any Holder. The Company or any of its Subsidiaries may act in any such capacity.

4. INDENTURE. The Company issued the Notes under an Indenture dated as of May 15, 2003 as supplemented by a First Supplemental Indenture dated as of May 15, 2003 (collectively, the “Indenture”) between the Company and the Trustee. The terms of the Notes include those stated in the Indenture and those made part of the Indenture by reference to the Trust Indenture Act of 1939, as amended (15 U.S. Code §§ 77aaa-77bbbb). The Notes are subject to all such terms, and Holders are referred to the Indenture and such Act for a statement of such terms. To the extent any provision of this Note conflicts with the express provisions of the Indenture, the provisions of the Indenture shall govern and be controlling. The Notes are obligations of the Company. The Company is issuing $55.0 million in aggregate principal amount on the date of this Note and may issue Additional Notes in accordance with the terms of the Indenture.

5. OPTIONAL REDEMPTION.

Optional Redemption. At any time on or after May 15, 2008, the Notes may be redeemed or purchased in whole or in part at the Company’s option at a price equal to 100% of the principal amount thereof plus the Applicable Premium as of, and accrued but unpaid interest, if any, to, the date of redemption or purchase (the “Redemption Date”) (subject to the right of Holders of record on the relevant record date to receive interest due on the relevant interest payment date). Such redemption or purchase may be made upon notice mailed by first-class mail to each Holder’s registered address, not less than 30 nor more than 60 days prior to the Redemption Date.

“Applicable Premium” means, with respect to a Note at any Redemption Date: (1) 104% of the principal amount of such Note if the Redemption Date is on or after May 15, 2008 and before May 15, 2009; (2) 102.667% of the principal amount of such Note if the Redemption Date is on or after May 15, 2009 and before May 15, 2010; (3) 101.333% of the principal amount of such Note if the Redemption Date is on or after May 15, 2010 and before May 15, 2011; and (4) 0% of the principal amount of such Note if the Redemption Date is on or after May 15, 2011. Calculation of the Applicable Premium will be made by the Company or on behalf of the Company by such Person as the Company shall designate; provided, however, that such calculation shall not be a duty or obligation of the Trustee.

“Treasury Rate” means, with respect to a Redemption Date, the yield to maturity at the time of computation of United States Treasury securities with a constant maturity (as compiled and published in the most recent Federal Reserve Statistical Release H.15(519) that has become publicly available at least two Business Days prior to such Redemption Date (or, if such Statistical Release is no longer published, any publicly available source of similar market data)) most nearly equal to the period from such Redemption Date to May 15, 2013; provided, however, that if the period from such Redemption Date to May 15, 2013 is not equal to the constant maturity of the United States Treasury security for which a weekly average yield is given, the Treasury Rate shall be obtained by linear interpolation (calculated to the nearest one-twelfth of a year) from the weekly average yields of United States Treasury securities for which such yields are given, except that if the period from such Redemption Date to May 15, 2013 is

less than one year, the weekly average yield on actually traded United States Treasury securities adjusted to a constant maturity of one year shall be used.

Optional Redemption Upon Equity Offerings. At any time, or from time to time, on or prior to May 15, 2006, the Company may, at its option, use the net cash proceeds of one or more Equity Offerings to redeem up to 35% of the principal amount of the Notes issued under the Indenture at a redemption price of 108% of the principal amount thereof plus accrued and unpaid interest thereon, if any, to the date of redemption; provided that:

6. MANDATORY REDEMPTION.

Except as set forth in paragraph 7 below, the Company shall not be required to make mandatory redemption payments with respect to the Notes.

7. REPURCHASE AT OPTION OF HOLDER.

Upon the occurrence of a Change of Control, the Company will be required to offer to purchase all of the outstanding Notes at a purchase price equal to 101% of the principal amount thereof, plus accrued and unpaid interest, if any, thereon to the date of repurchase.

8. NOTICE OF REDEMPTION. Notice of redemption will be mailed at least 30 days but not more than 60 days before the redemption date to each Holder whose Notes are to be redeemed at its registered address. Notes in denominations larger than $1,000 may be redeemed in part but only in whole multiples of $1,000, unless all of the Notes held by a Holder are to be redeemed. On and after the redemption date interest ceases to accrue on Notes or portions thereof called for redemption.

9. DENOMINATIONS AND TRANSFER. The Notes are in registered form without coupons in denominations of $1,000 and integral multiples of $1,000. The transfer of Notes may be registered and Notes may be exchanged as provided in the Indenture. The Registrar and the Trustee may require a Holder, among other things, to furnish appropriate endorsements and transfer documents and the Company and the Trustee may require a Holder to pay any taxes and fees required by law or permitted by the Indenture.

10. PERSONS DEEMED OWNERS. The registered Holder of a Note may be treated as its owner for all purposes.

11. AMENDMENT, SUPPLEMENT AND WAIVER. Subject to certain exceptions, the Indenture or the Notes may be amended or supplemented with the written consent of the Holders of at least a majority in principal amount of the then outstanding Notes voting as a single class, and any existing default or compliance with any provision of the Indenture or the Notes may be waived with the written consent of the Holders of a majority in principal amount of the then outstanding Notes voting as a single class. Without the consent of any Holder of a Note, the Indenture or the Notes may be amended or supplemented to cure any ambiguity, defect or inconsistency, to provide for certificated Notes in addition to or in place of uncertificated Notes, to provide for the assumption of the Company’s obligations to Holders of the Notes in case of a merger or consolidation, to make any change that would provide any additional rights or benefits to the Holders of the Notes or that does not adversely affect in any material respects the rights under the Indenture of any such Holder, to comply with the requirements of the Commission in order to effect or maintain the qualification of the Indenture under the Trust Indenture Act or to evidence and provide for the acceptance of appointment under the Indenture of a successor Trustee.

12. DEFAULTS AND REMEDIES. Events of Default are set forth in the Indenture. If any Event of Default occurs and is continuing, the Trustee or the Holders of at least 25% in principal amount of the then outstanding Notes may declare all the Notes to be due and payable. Notwithstanding the foregoing, in the case of an Event of Default arising from certain events of bankruptcy or insolvency, all outstanding Notes will become due and payable without further action or notice. Holders may not enforce the Indenture or the Notes except as provided in the Indenture. Subject to certain limitations, Holders of a majority in principal amount of the then outstanding Notes may direct the Trustee in writing in its exercise of any trust or power. The Trustee may withhold from Holders of the Notes notice of any continuing Default or Event of Default (except a Default or Event of Default relating to the payment of principal or interest) if it determines that withholding notice is in their interest. The Holders of a majority in aggregate principal amount of the Notes then outstanding by written notice to the Trustee may on behalf of the Holders of all of the Notes waive any existing Default or Event of Default and its consequences under the Indenture except a continuing Default or Event of Default in the payment of interest on, or the principal of, the Notes. The Company is required to deliver to the Trustee annually a statement regarding compliance with the Indenture, and the Company is required upon becoming aware of any Default or Event of Default, to deliver to the Trustee a statement specifying such Default or Event of Default.

13. TRUSTEE DEALINGS WITH COMPANY. The Trustee, in its individual or any other capacity, may make loans to, accept deposits from, and perform services for the Company or its Affiliates, and may otherwise deal with the Company or its Affiliates, as if it were not the Trustee.

14. NO RECOURSE AGAINST OTHERS. A director, officer, employee, incorporator or stockholder, of the Company, as such, shall not have any liability for any obligations of the Company under the Notes or the Indenture or for any claim based on, in respect of, or by reason of, such obligations or their creation. Each Holder by accepting a Note

waives and releases all such liability. The waiver and release are part of the consideration for the issuance of the Notes.

15. AUTHENTICATION. This Note shall not be valid until authenticated by the manual signature of the Trustee or an authenticating agent.

16. ABBREVIATIONS. Customary abbreviations may be used in the name of a Holder or an assignee, such as: TEN COM (= tenants in common), TEN ENT (= tenants by the entireties), JT TEN (= joint tenants with right of survivorship and not as tenants in common), CUST (= Custodian), and U/G/M/A (= Uniform Gifts to Minors Act).

17. CUSIP NUMBERS. Pursuant to a recommendation promulgated by the Committee on Uniform Security Identification Procedures, the Company has caused CUSIP numbers to be printed on the Notes and the Trustee may use CUSIP numbers in notices of redemption as a convenience to Holders. No representation is made as to the accuracy of such numbers either as printed on the Notes or as contained in any notice of redemption and reliance may be placed only on the other identification numbers placed thereon.

The Company will furnish to any Holder upon written request and without charge a copy of the Indenture. Requests may be made to:

Thornburg Mortgage, Inc.

150 Washington Avenue, Suite 302

Santa Fe, New Mexico 87501

Attention: Investor Relations

ASSIGNMENT FORM

To assign this Note, fill in the form below:

(I) or (we) assign and transfer this Note to:                                                                                                                                                                                   

                                                                                                              (Insert assignee’s legal name)

(Insert assignee’s soc. sec. or tax I.D. no.)

(Print or type assignee’s name, address and zip code)

and irrevocably appoint                                                                                                                                                                                                                         

to transfer this Note on the books of the Company. The agent may substitute another to act for him.

Date:                         

Signature Guarantee*:                         

* Participant in a recognized Signature Guarantee Medallion Program (or other signature guarantor acceptable to the Trustee).

OPTION OF HOLDER TO ELECT PURCHASE

If you want to elect to have this Note purchased by the Company pursuant to Section 4.15 of the First Supplemental Indenture, check the following box:    ¨

If you want to elect to have only part of the Note purchased by the Company pursuant to Section 4.15 of the First Supplemental Indenture, state the amount you elect to have purchased:

$                        

Date:                         

Signature Guarantee*:                         

* Participant in a recognized Signature Guarantee Medallion Program (or other signature guarantor acceptable to the Trustee).

ASSIGNMENT & TRANSFER CERTIFICATE

TO BE COMPLETED AND DELIVERED WITH THIS NOTE TO THE TRUSTEE IF THE UNDERSIGNED REGISTERED HOLDER WISHES TO SELL, ASSIGN AND TRANSFER NOTE:

In connection with the resale or other transfer of this Note occurring prior to the time the legend originally set forth on the face of this Note (or one or more predecessor Notes) restricting resales and other transfers thereof has been removed in accordance with the procedures set forth in the Indenture (other than a resale or other transfer made to the Company or to, by, through, or in a transaction approved by the Initial Purchaser), the undersigned registered holder certifies that without utilizing any general solicitation or general advertising:

[CHECK ONE]

If none of the foregoing boxes are checked, then, so long as this Note shall bear a legend on the face thereof restricting resales and other transfers thereof (except in the case of a resale or other transfer made to the Company or to, by, through, or in a transaction approved by, the Initial Purchaser), the Trustee shall not be obligated to register such Note in the name of any Person other than the registered holder thereof and until the conditions to any such registration of transfer set forth in this Note and in the Indenture shall have been satisfied.

TO BE COMPLETED BY TRANSFEREE

IF (a) ABOVE IS CHECKED:

The undersigned transferee represents and warrants that (i) it is a “qualified institutional buyer,” as defined in Rule 144A under the Securities Act of 1933, as amended, and acknowledges that the undersigned either has received such information regarding the Company as the undersigned transferee has requested pursuant to Rule 144A or has determined not to request such information, (ii) this instrument has been executed on behalf of the undersigned transferee by one of its executive officers and (iii) it is aware that the registered holder of this Note is relying upon the undersigned transferee’s foregoing representations in order to claim the exemption from registration provided by Rule 144A. The undersigned transferee acknowledges and agrees that this Note has not been registered under the Securities Act of 1933, as amended, and may not be transferred except in accordance with the resale and other transfer restrictions set forth in the legend on the face thereof.

TO BE COMPLETED BY TRANSFEREE

IF (b) ABOVE IS CHECKED:

The undersigned transferee represents and warrants that it is an institutional investor and an “accredited investor,” as defined in Rule 501(a)(1), (2), (3) or (7) under the Securities Act of 1933, as amended, and that this instrument has been executed on behalf of the undersigned transferee by one of its executive officers. The undersigned transferee undertakes to hold this Note acquired from the registered holder thereof for its own account, or as a fiduciary or agent for others (which others are also institutional accredited investors, unless such transferee is a bank acting in its fiduciary capacity), for investment purposes and not for distribution, subject to any requirement of law that the disposition of the undersigned transferee’s property shall at all times be and remain within its control. The undersigned acknowledges and agrees that this Note has not been registered under the Securities Act of 1933, as amended, and may not be transferred except in accordance with the resale and other transfer restrictions set forth in the legend on the face thereof.

TO BE COMPLETED BY TRANSFEREE

IF (c) ABOVE IS CHECKED:

The undersigned transferee represents and warrants that it is an institutional investor and that it is not a U.S. person (as defined in Regulation S under the Securities Act of 1933, as amended) and it is acquiring this Note from the registered holder thereof in an “offshore transaction” (as defined in Regulation S) pursuant to the exemption from registration under the Securities Act of 1933, as amended, provided by Regulation S thereunder. The undersigned transferee acknowledges and agrees that this Note has not been registered under the Securities Act of 1933, as amended, and may not be transferred except in accordance with the resale and other transfer restrictions set forth in the legend on the face thereof.