By John Poirier

WASHINGTON (Reuters) - The Federal Deposit Insurance Corp approved on Tuesday a proposal to help U.S. bank examiners better determine the amount of deposits at a large bank in the event of a failure.

FDIC Chairman Sheila Bair has repeatedly said the failure of a big U.S. bank is remote. But more financial institutions, trying to deal with big exposures to soured mortgage lending, are expected to become insolvent this year.

The new rules would require the largest banks to modify their deposit systems so the FDIC could quickly calculate how much it would need to pay out on deposits in insurance coverage if one failed. That would include requiring banks to determine the order of qualified depositors.

The rules would apply to banks with at least $2 billion in domestic deposits and either at least 250,000 deposit accounts or total assets of more than $20 billion. About 160 banks would be covered by the rules.

"That is really a critical authority that we need to deal with, with the eventuality of a large bank failure," FDIC Vice Chairman Martin Gruenberg said at an open meeting.

The FDIC has about 90 banks on its list of "troubled" institutions, but Bair recently told U.S. senators that future failures may include "institutions of greater size" than in the recent past.

The FDIC, which had about $53 billion at the end of March in the federal deposit insurance fund for use in the event of a bank failure, insures up to $100,000 per deposit and up to $250,000 per retirement account at insured banks.

The rules have been in the works for more than two years. They are aimed at instilling confidence in the banking industry by paying as soon as possible insured deposits and stemming any spillovers to other institutions.