BANK ONE ISSUANCE TRUST

Exhibit 1.1b

BANK ONE ISSUANCE TRUST

ONESERIES

CLASS B(2003-1) NOTES

TERMS AGREEMENT

Dated: April 4, 2003

To: Bank One, Delaware, National Association (the “Bank”)

Re: Underwriting Agreement dated April 4, 2003

Series Designation: ONEseries

Underwriters:

The Underwriters named on Schedule I attached hereto are the “Underwriters” for the purpose of this Agreement and for the purposes of the above referenced Underwriting Agreement as such Underwriting Agreement is incorporated herein and made a part hereof.

Terms of the Class B(2003-1) Notes:

Interest Payment Dates: The 15th of each month or if that day is not a Business Day, as defined in the Indenture, the next succeeding Business Day, commencing May 15, 2003.

Note Ratings: “A” by Standard & Poor’s Rating Services and Fitch, Inc. and “A2” by Moody’s Investors Service, Inc.

Indenture: The Indenture, dated as of May 1, 2002, between Bank One Issuance

Trust, by the Bank, as Beneficiary, Wells Fargo Bank Minnesota, National Association, as Indenture Trustee and acknowledged and accepted by the Bank, as Servicer.

Asset Pool One Supplement: The Asset Pool One Supplement, dated as of May 1, 2002, between Bank One Issuance Trust, by the Bank, as Beneficiary, and Wells Fargo Bank Minnesota, National Association, as Indenture Trustee and Collateral Agent and acknowledged by the Bank, as Transferor, Servicer and Administrator.

Indenture Supplement: The ONEseries Indenture Supplement, dated as of May 1, 2002, between Bank One Issuance Trust, by the Bank, as Beneficiary, and Wells Fargo Bank Minnesota, National Association, as Indenture Trustee and Collateral Agent.

Terms Document: The Class B(2003-1) Terms Document, dated as of April 15, 2003, between Bank One Issuance Trust, by the Bank, as Beneficiary and Wells Fargo Bank Minnesota, National Association, as Indenture Trustee and Collateral Agent.

Transfer and Servicing Agreement: The Transfer and Servicing Agreement, dated as of May 1, 2002, between Bank One Issuance Trust, by the Bank, as Beneficiary and Wells Fargo Bank Minnesota, National Association, as Indenture Trustee and Collateral Agent.

Pooling and Servicing Agreement: The Amended and Restated Pooling and Servicing Agreement, dated as of March 28, 2002, as may be further amended, between the Bank, as Transferor and Servicer, and The Bank of New York (Delaware), as trustee (the “Master Trust Trustee”).

Series Supplement: The Series 2002-CC Supplement, dated as of May 1, 2002, between the Bank, as Transferor and Servicer, and the Master Trust Trustee.

Purchase Price:

The purchase price payable by the Underwriters for the Notes covered by this Agreement will be the following percentage of the principal amounts to be issued:

Per Class B(2003-1) Note: 99.750%

Registration Statement: 333-67076.

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Underwriting Commissions, Concessions and Discounts:

The Underwriters’ discounts and commissions, the concessions that the Underwriters may allow to certain dealers, and the discounts that such dealers may reallow to certain other dealers, each expressed as a percentage of the principal amount of the Class B(2003-1) Notes, shall be as follows:

Underwriters’ Information: The information furnished by the Underwriters through the Representative for purposes of Section 9(b) of the Underwriting Agreement consists of the chart and the third and seventh paragraphs under the heading “Underwriting” in the Prospectus Supplement.

Closing Date: Pursuant to Rule 15c6-1(d) under the Securities Exchange Act of 1934, as amended, the Underwriters, the Bank and the Issuer hereby agree that the Closing Date shall be April 15, 2003, 9:00 a.m., New York Time.

Location of Closing: Skadden, Arps, Slate, Meagher & Flom LLP, Four Times Square, New York, New York 10036.

Payment for the Notes:

The Underwriters agree, severally and not jointly, subject to the terms and provisions of the above referenced Underwriting Agreement which is incorporated herein in its entirety and made a part hereof, to purchase the respective principal amounts of the above referenced Class B(2003-1) Notes set forth opposite their names on Schedule I hereto.

Representations of the Underwriters:

Each Underwriter of the Class B(2003-1) Notes has represented and agreed that: (a) it has not offered or sold, and prior to the date which is six months after the date of issue of the Class B(2003-1) Notes, will not offer or sell any Class B(2003-1) Notes to persons in the United Kingdom except to persons whose ordinary activities involve them in acquiring, holding, managing or disposing of investments (as principal or agent) for the purposes of their businesses or otherwise in circumstances which do not constitute an offer to the public in the United Kingdom for the purposes

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of the Public Offers of Securities Regulations 1995; (b) it has complied and will comply with all applicable provisions of the Financial Services and Markets Act 2000 (the “FSMA”) with respect to anything done by it in relation to the Class B(2003-1) Notes in, from or otherwise involving the United Kingdom; and (c) it has only communicated or caused to be communicated and it will only communicate or cause to be communicated any invitation or inducement to engage in investment activity (within the meaning of section 21 of the FSMA) received by it in connection with the issue or sale of any Class B(2003-1) Notes in circumstances in which section 21(1) of the FSMA does not apply to the Issuer.

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Accepted:

BANK ONE, DELAWARE, NATIONAL ASSOCIATION,

as Transferor and Servicer

[Signature Page to the Bank One Issuance

Trust (ONEseries Class B(2003-1)) Terms Agreement]

SCHEDULE I

UNDERWRITERS

$200,000,000 Principal Amount of ONEseries Class B(2003-1) Notes