WASHINGTON (Reuters) - The Federal Reserve on Monday announced that smaller lenders will be exempted from parts of a rigorous "stress test" of their financial health in a move that had been expected.

Last year, 33 firms underwent a "qualitative" exam of back office functions but that number will be pared to 13 lenders, the Fed said.

The rule is meant to remove a "significant burden on these firms" and put the toughest checks on the largest banks, the Fed said.

The Fed had signaled the move last year. The annual stress test is a check on whether financial firms have capital reserves to weather an economic downturn.

(Reporting By Patrick Rucker; Editing by Meredith Mazzilli)