An man convicted of murdering a woman after breaking into her apartment as she slept was put to death Thursday evening in Alabama in the nation’s fourth execution using nitrogen gas.

A federal judge on Friday refused to stop what would be the fourth nitrogen gas execution in the U.S., saying the inmate had not proven his claims that the new method is unconstitutionally cruel and causes psychological terror.

Alabama is planning to carry out its fourth execution with nitrogen gas. Demetrius Terrence Frazier is scheduled to be executed Feb. 6 at a south Alabama prison. Frazier was convicted of killing 41-year-old Pauline Brown in 1991.