The way banks process checks – widely blamed for running up excessive overdraft fees on consumers – is being targeted in a new bill to be introduced by Ohio Sen.Sherrod Brownthe Cleveland Plain Dealerreports.

Many banks process payments "high-to-low," with the largest amounts first, which can subject more transactions to overdraft fees that average $34 each at the country's largest institutions, according to astudy of the practice released last monthby the Consumer Financial Protection Bureau. That same study found that bounced-check fees totaled more than $32 billion in 2012, representing 77 percent of deposit account service charges and fee income at many banks.

Sen. Brown's bill could change that. It would require banks to be more transparent about how they process transactions so customers could make educated decisions about where to bank, the Plain Dealer reported. He'd direct the CFPB to come up with a model that's fair to banks and their customers, the paper said, and would give banks protection against lawsuits for following that model.

He's expected to explain the bill at a press conference in Cleveland.

Huntington National Bank (NASDAQ:HBAN) this year changed the way it posts transactions to checking accounts, doing so primarily in chronological order, which it said would cost it up to $30 million in fees per year