Fallin on Tuesday ordered the Department of Corrections to review the state's execution procedures and determine what happened during the execution of Clayton Lockett.
Lockett shook uncontrollably, writhed on the gurney and gritted his teeth for several minutes after the execution began using a new three-drug combination. Department of Corrections Director Robert Patton stopped the execution after he said a doctor determined Lockett's vein failed.
Patton said Lockett was pronounced dead of a heart attack about 45 minutes after the execution began.
A second inmate, Charles Warner, had been scheduled to die later Tuesday.