Biros died at 11:47 a.m. after a one-drug lethal injection, a method never used before on humans, per the New York Times.
The new method has been somewhat controversial as it involves a slower execution. Typically a three-drug process is used.
The process experimented with involves thiopental sodium, which puts people so deeply to sleep that they stop breathing and it is estimated to take just under 15 minutes.
Lawyers had been trying to fight the use, which they condemned as human experimentation.
Biros was sentenced to death for killing and dismembering a woman he met at a bar in 1991.