SEAGATE TECHNOLOGY and U.S. BANK NATIONALASSOCIATION TRUSTEE FIRST SUPPLEMENTAL INDENTURE Dated as of May 19, 2006 Supplementing the Indenture dated as of May 7, 2003

EXHIBIT 10.4

MAXTOR CORPORATION

SEAGATE TECHNOLOGY

and

U.S. BANK NATIONAL ASSOCIATION

TRUSTEE

FIRST SUPPLEMENTAL INDENTURE

Dated as of May 19, 2006

Supplementing the Indenture dated as of May 7, 2003

FIRST SUPPLEMENTAL INDENTURE, dated as of May 19, 2006 (this “First Supplemental Indenture”), by and among MAXTOR CORPORATION, a Delaware corporation (the “Company”), SEAGATE TECHNOLOGY, an exempted company incorporated with limited liability under the laws of the Cayman Islands (“Parent”), and U.S. BANK NATIONAL ASSOCIATION, as Trustee (the “Trustee”).

RECITALS

WHEREAS, the Company has heretofore executed and delivered to the Trustee an Indenture, dated as of May 7, 2003 (the “Indenture”), providing for the creation and issuance by the Company of 6.80% Convertible Senior Notes due 2010 (the “Securities”).

WHEREAS, the Company and Parent have entered into an Agreement and Plan of Merger, dated as of December 20, 2005 (the “Merger Agreement”), by and among the Company, Parent, and MD Merger Corporation, a Delaware corporation and a direct wholly-owned subsidiary of Parent (“Sub”), pursuant to which: (i) Sub will merge with and into the Company (the “Merger”); (ii) each issued and outstanding share of the Company’s Common Stock (other than the Cancelled Shares (as defined in the Merger Agreement)) outstanding immediately prior to the effective time of the Merger (the “Effective Time”) will be converted into the right to receive common stock of Parent; and (iii) the Company will continue as the surviving and continuing corporation and succeed to and assume all the rights and obligations of Sub in accordance with the Delaware General Corporations Law.

WHEREAS, pursuant to Sections 5.01 and 10.05 of the Indenture, the Company, Parent and Trustee have agreed in connection with the Merger to execute this First Supplemental Indenture to make the Securities convertible into cash and shares of the common stock of Parent and to provide for the full and unconditional guaranty by Parent of the Company’s obligations to the Holders of Securities.

WHEREAS, Sections 9.01(c) and 9.01(d) of the Indenture provide that the parties hereto may execute this First Supplemental Indenture without the consent of Holders of the Securities.

WHEREAS, in accordance with Section 9.06 of the Indenture the Trustee is authorized to execute and deliver this First Supplemental Indenture.

WHEREAS, in accordance with Sections 5.01(c) and 11.04(1) and (2) of the Indenture, the Trustee has received an Officers’ Certificate and an Opinion of Counsel relating to the Merger and this Supplemental Indenture.

NOW, THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt of which is hereby acknowledged, the Company, Parent and the Trustee, acting for itself and the Holders of the Securities, agree as follows:

1. Defined Terms. In this First Supplemental Indenture, unless the context otherwise requires:

1.1 terms defined in the Indenture have the same meaning when used in this First Supplemental Indenture unless otherwise defined in this First Supplemental Indenture; and

1.2 all references to “the First Supplemental Indenture” or “this First Supplemental Indenture” are to this First Supplemental Indenture as modified, supplemented or amended from time to time.

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2. Amendments to the Indenture.

2.1 Section 1.1. Section 1.1 of the Indenture is hereby amended by inserting each of the following definitions in place of the corresponding definition of such term in the Indenture or, where no definition for such term is provided in the Indenture, inserting the following definitions as new defined terms in appropriate alphabetical order:

“Applicable Stock” means (i) the Common Stock and (ii) in the event of a merger, consolidation or any other transaction of the type described in Section 10.05 involving Parent that is otherwise permitted hereunder in which Parent is not the surviving corporation, the common stock of such surviving corporation or its direct or indirect parent corporation.

“Board of Directors” means either the Board of Directors of the Company or Parent, as the case may be, or any duly authorized committee of such board.

“Common Stock” means the common shares, par value $0.00001 per share, of Parent of the type authorized on the date of the First Supplemental Indenture, or any other shares of Capital Stock of Parent into which such Common Stock shall be reclassified or changed.

“Officer” means the Chairman of the Board, the Chief Executive Officer, the Chief Financial Officer, the President, any Vice President, the Treasurer, the Assistant Treasurer, the Secretary or any Assistant Secretary of the Company or Parent, as the case may be.

“Officers’ Certificate” when used with respect to the Company or Parent, as the case may be, means a written certificate containing the information specified in Sections 11.04 or 11.05, signed in the name of the Company or Parent, as applicable, by any two Officers and delivered to the Trustee. An Officers’ Certificate given pursuant to Section 4.03 shall be signed by the Chief Executive Officer, President, Chief Financial Officer or other authorized financial or accounting Officer of the Company or Parent, as the case may be, but need not contain the information specified in Sections 11.04 and 11.05.

“Opinion of Counsel” means a written opinion containing the information specified in Sections 11.04 and 11.05, from legal counsel who is reasonably acceptable to the Trustee. The counsel may be an employee of, or counsel to, the Company, Parent or the Trustee.

“Parent” means Seagate Technology, an exempted company incorporated with limited liability under the laws of the Cayman Islands, and its successors and assigns.

“Parent Subsidiary” means (i) a corporation, a majority of whose outstanding Voting Stock is, at the date of determination, directly or indirectly owned by Parent, by one or more Parent Subsidiaries or by Parent and one or more Parent Subsidiaries, (ii) a partnership in which Parent or a Parent holds a majority interest in the equity capital or profits of such partnership, or (iii) any other Person (other than a corporation) in which Parent, a Parent Subsidiary or Parent and one or more Parent Subsidiaries, directly or indirectly, at the date of determination, has (x) at least a majority ownership interest or (y) the power to elect or direct the election of a majority of the directors or other governing body of such Person.

“Sale Price” means, with respect to any security on any day, (1) the closing sale price per share on such day (or if no closing sale price is reported, the average of the reported closing bid and asked prices or, if more than one in either case, the average of the average closing bid and the average closing ask prices) as reported in composite transactions for the principal United States

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national or regional securities exchange on which such security is traded, or (2) if such security is not listed on a United States national or regional securities exchange, as reported by the National Association of Securities Dealers Automated Quotation System, or (3) if not so reported, the average of the closing bid and ask prices of such security on the over-the-counter market on the day in question as reported by the National Quotation Bureau Incorporated, or (4) in the case of Common Stock only, if not so quoted, the Sale Price will be the average of the mid-point of the last bid and asked prices for the Common Stock on the relevant date from each of at least three nationally recognized independent investment banking firms selected by the Company or Parent for this purpose, or (5) a price determined in good faith by the Board of Directors or, to the extent permitted by applicable law, a duly authorized committee thereof, whose determination shall be conclusive.

2.2 Article 3

(a) Section 3.09(c). Section 3.09(c) of the Indenture is hereby amended by replacing the words “the Company” the third time they appear with “Parent”.

(b) Section 3.09(c)(ii)(5). Section 3.09(c)(ii)(5) of the Indenture is hereby amended by replacing the words “issued by the Company” in clause (B) thereof, with “issued by Parent”.

(c) Section 3.10. Section 3.10 of the Indenture is hereby amended by replacing the words “the Company” with “Parent”.

(d) Section 3.13. Section 3.13 of the Indenture is hereby amended by adding the words “or Parent, as the case may be,” after the words “the Company” the first time they appear and by replacing the words “the Company” with “Parent” the second time they appear in the second unnumbered paragraph of Section 3.13.

(e) Section 3.15. Section 3.15 of the Indenture is hereby amended by adding the words “and Parent” after the words “the Company”.

(f) Section 3.16. Section 3.16 of the Indenture is hereby amended by inserting the words “to Parent any” after the words “to the Company any cash or”; by inserting the words “and Parent” after the words “the Company” the second time they appear; and by inserting the words “or Parent, as the case may be,” after the words “the Company” the fifth time they appear.

2.3 Article 4

(a) Section 4.01. Section 4.01 of the Indenture is hereby amended by inserting the following as a new paragraph at the end of Section 4.01:

Parent hereby irrevocably and fully and unconditionally guarantees all of the Company’s obligations under the Securities and under this Indenture, including without limitation, the due and punctual payment of the principal of and interest (including Liquidated Damages, if any) on all of the Securities and the performance of every covenant of this Indenture and in the Securities to be performed or observed by the Company.

(b) Section 4.02. The words “and Parent” are hereby inserted after the word “Company” the first time it appears in the first sentence, and each time it appears in the fourth and fifth sentences of Section 4.02 of the Indenture. The words “or Parent” are hereby inserted after the word “Company” the second time it appears in the first sentence and each time it appears in the second and third sentences of Section 4.02 of the Indenture.

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(c) Section 4.03. The words “and Parent” are hereby inserted after the word “Company” the first and second times it appears in Section 4.03 of the Indenture. The words “or Parent” are hereby inserted after the word “Company” the third and fourth times it appears in Section 4.03 of the Indenture.

(d) Sections 4.04. The words “and Parent” are hereby inserted after the word “Company” each time it appears in Section 4.04 of the Indenture.

(e) Section 4.06. The words “or Parent” are hereby inserted after the word “Company” the first time it appears in Section 4.06 of the Indenture. The words “or Parent, as the case may be,” are hereby inserted after the word “Company” the second time it appears in Section 4.06 of the Indenture.

2.4 Article 5. Article 5 of the Indenture is amended in its entirety to read as follows:

ARTICLE 5

SUCCESSOR PERSON

Section 5.01 When Company or Parent May Merge Or Transfer Assets. Neither the Company nor Parent shall consolidate with or merge with or into any other Person or convey, transfer, sell, lease or otherwise dispose of all or substantially all of its properties and assets to any Person, unless:

(a) either (1) in the case of a consolidation or merger of the Company, the Company shall be the continuing corporation, or in the case of a consolidation or merger of Parent, Parent shall be the continuing corporation, or (2) the Person (if other than the Company or Parent, as the case may be) formed by such consolidation or into which the Company or Parent, as the case may be, is merged or the Person that acquires by conveyance, transfer or lease all or substantially all of the properties and assets of the Company or Parent, as the case may be, (i) shall be organized and validly existing under the laws of the United States or any State thereof or the District of Columbia and (ii) shall expressly assume, by an indenture supplemental hereto, executed and delivered to the Trustee, in form reasonably satisfactory to the Trustee, all of the obligations of the Company or Parent, as the case may be, under the Securities and this Indenture;

(b) immediately after giving effect to such transaction, no Event of Default, and no event that, after notice or lapse of time or both, would become an Event of Default, shall have occurred and be continuing; and

(c) the Company or Parent, as the case may be, shall have delivered to the Trustee an Officers’ Certificate and an Opinion of Counsel, each stating that such consolidation, merger, conveyance, transfer or lease and, if a supplemental indenture is required in connection with such transaction, such supplemental indenture, comply with this Article 5 and that all conditions precedent herein provided for relating to such transaction have been satisfied.

For purposes of the foregoing, the transfer (by lease, assignment, sale or otherwise) of the properties and assets of one or more Subsidiaries (other than to the Company or another Subsidiary), which, if such assets were owned by the Company, would constitute substantially all of the properties and assets of the Company, shall be deemed to be the transfer of substantially all

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of the properties and assets of the Company. For purposes of the foregoing, the transfer (by lease, assignment, sale or otherwise) of the properties and assets of one or more Parent Subsidiaries (other than to Parent or another Parent Subsidiary), which, if such assets were owned by Parent, would constitute substantially all of the properties and assets of Parent, shall be deemed to be the transfer of substantially all of the properties and assets of Parent.

The successor Person formed by such consolidation or into which the Company or Parent, as the case may be, is merged or the successor Person to which such conveyance, transfer or lease is made shall succeed to, and be substituted for, and may exercise every right and power of, the Company or Parent, as the case may be, under this Indenture with the same effect as if such successor had been named as the Company or Parent, as the case may be, herein; and thereafter, except in the case of a lease and obligations the Company or Parent, as the case may be, may have under a supplemental indenture, the Company or Parent, as the case may be, shall be discharged from all obligations and covenants under this Indenture and the Securities. Subject to Section 9.06, the Company, Parent, the Trustee and the successor Person shall enter into a supplemental indenture to evidence the succession and substitution of such successor Person and such discharge and release of the Company or Parent, as the case may be.

2.5 Article 6.

(a) Section 6.01(1). Section 6.01(1) of the Indenture is hereby amended in its entirety to read as follows:

(1) following the exercise by the Holder of the right to convert a Security in accordance with Article 10 hereof, (x) the Company or Parent fails to deliver the cash, if any, required to be delivered as part of the applicable Conversion Settlement Distribution on the applicable Conversion Settlement Date and such failure continues for ten days or (y) Parent fails to deliver the Common Stock required to be delivered as part of the applicable Conversion Settlement Distribution as required pursuant to Section 10.02(d)(ii);

(b) Section 6.01(6). The words “or Parent” are hereby inserted after the word “Company” each time it appears in Section 6.01(6) of the Indenture.

2.6 Article 9. The word “, Parent” is inserted after the word Company in the preamble to Section 9.01 of the Indenture. The words “or Parent” are hereby inserted after the word “Company” in Sections 9.01(a), 9.01(b), 9.01(g), 9.01(h), 9.01(i) and 9.02. The words “or Parent’s” are hereby inserted after the word “Company’s” in Sections 9.01(c) and 9.01(d).

2.7 Article 10.

(a) Section 10.01. The words “and Parent’s” are hereby inserted after the word “Company’s” the first time it appears in the last sentence of Section 10.01 of the Indenture.

(b) Section 10.02(a). The second sentence of Section 10.02(a) of the Indenture is hereby amended in its entirety to read as follows:

The rate at which shares of Common Stock shall be delivered upon conversion (the “Conversion Rate”) shall be initially 30.1733 shares of Common Stock for each $1,000 principal amount of Securities.

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The last sentence of Section 10.02(a) of the Indenture is hereby amended by replacing the words “The Company” with “Parent”.

(c) Sections 10.04, 10.05, 10.06, 10.07, 10.08 and 10.11. The words “the Company” are hereby replaced with the word “Parent”, each time they appear in Sections 10.04 (other than the first time they appear in Section 10.04(i)), 10.05, 10.06, 10.07 and 10.10 of the Indenture.

(d) Section 10.08. The words “or Parent” are hereby inserted after the word “Company” each time it appears in Section 10.08 of the Indenture.

(e) Section 10.09. The words “the Company” are hereby replaced with the word “Parent”, each time they appear in Section 10.10(a) and (b) and the first time they appear in Section 10.10(c). The words “or Parent” are hereby inserted after the word “Company” the second, third and fourth time it appears in Section 10.10(c) and each time it appears in Section 10.10(d) of the Indenture.

2.8 Article 11.

(a) Section 11.02. Section 11.02 of the Indenture is hereby amended in its entirety to read as follows:

11.02 Notices. Any request, demand, authorization, notice, waiver, consent or communication shall be in writing and delivered in person or mailed by first-class mail, postage prepaid, addressed as follows or transmitted by facsimile transmission (confirmed by guaranteed overnight courier) to the following facsimile numbers:

if to the Company:

Maxtor Corporation

500 McCarthy Boulevard

Milpitas, CA 95035

Attn: General Counsel

Fax: 303 ###-###-####

if to Parent:

Seagate Technology

920 Disc Drive

P.O. Box 66360

Scotts Valley, California 95067

Attn: General Counsel

Fax: 831 ###-###-####

if to the Trustee:

U.S. Bank National Association

633 West Fifth Street, 24^th Floor

Los Angeles, CA 90071

Attn: Corporate Trust Services

(Maxtor Corporation 6.80% Convertible Senior Notes due 2010)

Fax: 213 ###-###-####

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The Company, Parent or the Trustee by notice given to the others in the manner provided above may designate additional or different addresses for subsequent notices or communications.

Any notice or communication given to a Securityholder shall be mailed to the Securityholder, by first-class mail, postage prepaid, at the Securityholder’s address as it appears on the registration books of the Registrar and shall be sufficiently given if so mailed within the time prescribed.

Failure to mail a notice or communication to a Securityholder or any defect in it shall not affect its sufficiency with respect to other Securityholders. If a notice or communication is mailed in the manner provided above, it is duly given, whether or not received by the addressee.

If the Company mails a notice or communication to the Securityholders, it shall mail a copy to the Trustee and each Registrar, Paying Agent, Conversion Agent or co-registrar.

(b) Section 11.11. The first sentence of Section 11.11 is hereby replaced with the following sentence: “All agreements of the Company and Parent in this Indenture and the Securities shall bind their respective successors.”

3. Miscellaneous.

3.1 Except as expressly amended hereby, the Indenture is in all respects ratified and confirmed and all terms, conditions and provisions thereof shall remain in full force and effect. This First Supplemental Indenture shall be construed as supplemental to the Indenture and all the terms and conditions of this First Supplemental Indenture shall be deemed part of the terms and conditions of the Indenture. Every holder of Securities heretofore or hereafter authenticated and delivered shall be bound hereby. This First Supplemental Indenture is subject to the provisions of the Trust Indenture Act, and shall, to the extent applicable, be governed by such provisions.

3.2 This instrument may be executed in any number of counterparts, each of which shall be an original; but such counterparts shall together constitute but one and the same instrument.

3.3 The Article and Section headings herein are for convenience only and shall not affect the construction hereof.

3.4 In case any one or more of the provisions contained in this First Supplemental Indenture or in the Securities shall for any reason be held to be invalid, illegal or unenforceable in any respect, such invalidity, illegality or unenforceability shall not effect any other provisions of this First Supplemental Indenture or of the Securities, but this First Supplemental Indenture and the Securities shall be construed as if such invalid or illegal or unenforceable provision had never been contained herein or therein.

3.5 THIS FIRST SUPPLEMENTAL INDENTURE SHALL BE CONSTRUED IN ACCORDANCE WITH THE LAW OF THE STATE OF NEW YORK.

3.6 No amendment to or termination of this First Supplemental Indenture and no modification of the Company’s or Parent’s respective obligations under the Indenture and this First Supplemental Indenture shall be effective absent the written consent of the Company, the Trustee and Parent.

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3.7 The Trustee shall not be responsible in any manner whatsoever for or in respect of the validity or sufficiency of this First Supplemental Indenture or for or in respect of the recitals contained herein.

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

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