In the US state's first use of the death penalty in 12 years, Arkansas had executed Ledell Lee.
It is the first of a series of executions expected after the state Supreme Court overturned a lower court ruling blocking the use of a lethal injection.
Justices reversed the ban on the use of vecuronium bromide, one of the three drugs used by the state.
Lee's third request to stay the execution was denied.
Instead of a last meal, he asked to receive communion, said an official.
The state had planned to carry out eight executions in 11 days, before its supply of the lethal injection drug, midazolam, expired on 30 April.
The first three executions were cancelled due to various court rulings.
Lee told the BBC in a recent interview that he was innocent of the murder of Debra Reese, and death row was like a "living nightmare".
The other inmate due to die on Thursday has been given a stay to make time for advanced DNA testing that his lawyers say could prove his innocence.
Stacey Johnson was convicted of the murder of Carol Heath, who was beaten and had her throat slit in her flat in 1993.
The ruling on Thursday paves the way for the series of executions the state had planned this month.
Like many US states, Arkansas has struggled to find the drugs it needs to carry out executions. Its last was in 2005.
Source: News Agencies, Edited by website team