The U.S. is a prisoner of out-of-date mechanisms to handle bad banks, Federal Deposit Insurance Corporation (FDIC) Chairwoman Sheila Bair said Monday, calling for a new insurance fund in which banks -- not taxpayers -- would fund firms' restructuring.

"We can't let ourselves be prisoners of out-dated authorities, trapped in a resolution regime which pre-dated the evolution of the 'shadow banking sector,'" Bair argued in a speech before the Economic Club of New York.

The chairwoman called for a new "resolution regime" headed by the FDIC that would wind down banks with troubled balance sheets at a minimal cost to the American taxpayer.

"A new resolution authority could include assessments on larger firms to fund a reserve that would be tapped to absorb losses for a failure," Bair said Monday. "I believe it's only fair that the industry that benefits should pay -- just as banks pay for deposit insurance."

Bair said those fees for firms would be based on a variety of factors, including its size and the riskiness of its investments (with higher-risk companies incurring larger fees).

"We cannot effectively solve the problems caused by the too big to fail notion unless we overhaul how we regulate and supervise big institutions, and how we resolve them when they implode," Bair explained. "The sooner we modernize our resolution structure, the sooner we can end to big too fail, and clear the way for a stronger, brighter and more stable economic future."