Charles Singleton, 44, a diagnosed schizophrenic was given a lethal injection on Tuesday in the state's death chamber in Varner, about 115km southeast of Little Rock, for stabbing white grocery store clerk Mary Lou York to death in 1979.
Another prisoner Karl Roberts, 35, was put to death after Singleton for raping and killing his 12-year-old niece.
Lawyers for Roberts filed a last-minute appeal requesting a temporary stay of execution, which was granted by a federal court.
Arkansas governor Mike Huckabee said he would not issue a stay for Singleton, who had run out of appeals.
Several groups such as the European Union and Amnesty International petitioned the governor to commute the death sentence, saying it was morally reprehensible to execute a person with a severe mental illness.
While in prison, Singleton's mental condition worsened and he was forcibly given powerful drugs to curtail his psychotic episodes, under a 1990 US Supreme Court decision that allows states to forcibly medicate a prisoner if that person is a danger to himself or others, and the treatment is in that person's medical interest.
According to Amnesty International, Singleton was likely suffering from schizophrenia.
"By the late 1980s he had begun to suffer delusions, including that his cell was possessed by demons, that a prison doctor had implanted a device in his ear, and that his thoughts were being stolen when he read the Bible," said the human rights watchdog.
Lawyers for Singleton appealed to have the medication stopped, saying that it was not in their client's medical interest to be declared mentally competent enough to be executed.
Last year, the Eighth Circuit federal court ruled that Arkansas could forcibly medicate Singleton. In the decision, the court said that "eligibility for execution is the only unwanted consequence of the medication."
The US Supreme Court refused to hear an appeal of the
lower court's decision.
The Supreme Court has ruled that states cannot execute mentally retarded prisoners or those whose mental illness makes it impossible for them to understand that they are going to be put to death.
The race factor
Amnesty said execution was
Singleton was tried in front of an all-white jury for the murder of a white woman. According to Amnesty International, at least one in five of the 300 African-Americans executed in the US since 1977 were tried in front of all-white juries.
Eighty per cent of the more than 880 people put to death since 1977, were convicted of crimes involving whites, even though whites and blacks are the victims of murder in almost equal numbers, it added.
Race of murder victim has been shown to be a factor in capital sentencing in the US. The odds of a death sentence in cases in which blacks killed whites has been shown to be as much as 11 times higher than in the murder of a black victim by a white person, according to Amnesty.
Another execution of a black prisoner took place in the US on the same day.
Ynobe Matthews was declared dead at 00:16 GMT on Wednesday of a lethal injection which was administered eight minutes earlier at the Texas State Penitentiary in Huntsville.
Prison spokeswoman Michelle Lyons said Matthews, 27, convicted of the May 2000 rape and murder of a 21-year-old white woman, whose house he then set alight, died without making a final statement.
A handful of anti-death penalty protesters demonstrated outside.
Matthews has renounced the long appeals that are normally filed on behalf of death row inmates in order, he said, to spare his and his victim's families from further anguish.