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.

They also seek to clarify how some deposits swept into a different investment product would be treated.

The possibility of commercial bank failures has been a big topic among regulators and lawmakers in Washington, who are carefully watching how the banking industry is being impacted by the housing and credit problems.

In mid-May Bair also proposed creating a federal mechanism to close down an investment bank if another such institution spirals down toward insolvency by possibly applying some of the existing regulatory framework for commercial banks.

Bair is expected to further discuss the regulation of investment banks in a speech on Wednesday before the Exchequer Club, a group of financial professionals, in Washington.

Some banking trade associations have complained the cost of implementing the rules would outweigh the benefits because of the perception of an extremely low likelihood of a big bank failure.

The FDIC cited a comment from an unnamed bank regulatory agency that highlighted the importance of advanced preparation in case a big bank fails.

The regulatory agency said, “Several very large financial institutions moved from reasonably strong financial positions to what observers characterized as near failure in short periods of time,” according to a copy of the FDIC rules.