Security First Network Bank, which bills itself as an "Internet-only" bank, has expanded into the proprietary on-line arena, forming a partnership with Compuserve Inc.

Under terms of an agreement between the bank and the consumer computer service, members of Columbus, Ohio-based Compuserve can open accounts with Security First and pay bills electronically.

To stimulate interest among Compuserve's more than four million members, the bank and the on-line service are offering new customers of Security First $40 worth of time on Compuserve's network.

Security First spokeswoman Kim Humphreys said her Pineville, Ky.-based institution is "the first bank going live in Compuserve's banking center."

"We want to make it easy for people who do want to access the bank through an on-line service," she said. Compuserve "has upgraded their service to help simplify this."

Compuserve, a unit of H&R Block Inc., is not the only network of its kind working with banks.

The largest of the on-line services, America Online Inc., Vienna, Va., recently announced a relationship with BankAmerica Corp. In addition, Intuit Inc., which makes personal finance software, has announced plans to make home banking services available over the network.

Prodigy Services Co., the third of the major on-line services, also offers home banking in conjunction with several financial institutions.

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