Concerned that customers may be scared away by perceived security problems on the Internet, several on-line financial institutions have taken out hacker insurance.

The SafeWeb Remote Banking policy, from a unit of Travelers Property Casualty Corp., is designed to protect consumers from loss through unauthorized on-line transactions.

Compubank of Houston is offering the coverage free. It has just opened for business exclusively via the Internet and telephone.

NCR Corp. has bought the insurance on behalf of customers using its Internet software, which include the all-Internet institution NetBank of Atlanta, Coastal Federal Savings Bank of Myrtle Beach, S.C., and Nantucket Bank in Massachusetts.

Customers banking on-line are already protected by the Federal Reserve's Regulation E, which limits liability for unauthorized transactions. The insurance is designed to further ease customers' fears.

"We doubt very much that we will ever have a claim against this," said Gregory A. Hanson, general manager of electronic commerce solutions at NCR. It is mainly "about perception and increasing confidence."

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