Jeffrey P. Gaia, a former division president at Bank One Corp., is a traditional type of banker — not the sort who might be expected to jump ship for an Internet-only bank, especially now that the dot-com bubble has burst.

And yet Mr. Gaia, who has spent his career lending to small businesses and offering home loans and most recently ran a $13 billion-a-year unit, last week became the first president of a Web-only institution called National InterBank, which opened in 1999 and has $90 million of assets. He had been out of a job for several months.

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