TALLAHASSEE -- A bill meant to give prisoners who might be innocent a better chance to clear themselves through DNA testing passed the House on Wednesday and is headed to Gov. Jeb Bush.

The bill would give prisoners two years after their sentence becomes final to ask a judge to order testing of genetic material from the crime scene if they can show it could help them prove they are innocent.

Sponsored by Rep. Randy Ball, a former homicide investigator, and Sen. Alex Villalobos, a former prosecutor, the bill comes in the wake of several cases in which DNA evidence has exonerated prisoners in Florida.

The bill, CS-SB 366, passed 118-0 in the House, a day after passing the Senate 37-0.

It would also expand the state's DNA database to include convicted robbers next year and later all serious felons.

The Florida Department of Law Enforcement already collects samples of genetic material from rapists, murderers, burglars and other violent criminals to check it against evidence from crime scenes.

The bill also provides for testing of inmates before they are released to provide one more group whose DNA could be matched against that collected at future crime scenes.

But the main part of the measure was meant to increase innocent prisoners' chances of being exonerated.

The bill was filed after the case of inmate Frank Lee Smith, who died last year after spending 14 years on Death Row. DNA tests completed after his death proved him innocent.