WASHINGTON: A convict in Texas is facing execution today unless the US Supreme Court and the state's governor accept his last-minute appeal for DNA testing that he says will show his innocence. Henry "Hank" Skinner, 47, has pleaded unsuccessfully in the past for authorities to redo DNA tests which he says will show he did not commit the New Year's Eve 1993 murder of his girlfriend and her two sons in his home. He was sentenced to death after a jury trial in 1995, but he contends that additional DNA testing on items that were not examined during his trial would show his innocence. On Sunday, the Texas Board of Pardon and Paroles rejected Skinner's request, leaving his fate in the hands of the US Supreme Court and Texas Governor Rick Perry. "I can't think of any good reason why you would refuse to do DNA testing in a case where there is other strong evidence pointing to innocence," Skinner's attorney Rob Owen told AFP. "If I were a prosecutor I wouldn't want to put someone to death before I was absolutely sure -- and in this case, the DNA testing is what we need to be sure." He said his client remains optimistic and confident that his request might be granted, even as the hours ticked down to his execution. Skinner, who is married to a French anti-death penalty campaigner, has proclaimed his innocence since his arrest. Ten years ago he attracted the support of David Protess, a journalism professor at Northwestern University, who re-examined the case with his students. Their conclusion, based on comparisons of Skinner's DNA and that found on his victims, was that Skinner is innocent. Some DNA evidence was presented during Skinner's trial to ascertain that he had been present in his home in the Texas Panhandle town of Pampa when the murders were committed -- a point that the defence never contested. However, blood tests after his arrest established that Skinner was under the influence of anti-anxiety medication, painkillers and alcohol at the time of the murders. He thus would have been physically unable to commit the murders, in which girlfriend Twila Jean Busby, 40, was fatally beaten with an axe handle and her two sons aged 20 and 22 stabbed to death, his defence team argues. "There was no confession... no eyewitness to the crime, no apparent motive, no pattern of violence by Mr Skinner," Protess wrote in a letter to the Texas Board of Pardon and Paroles. The journalism professor also noted that Skinner's alleged victim had complained on the night of the murder of being harassed by her uncle, who was not questioned during the investigation into her murder. Skinner's request comes after the Supreme Court justices ruled last year, by a vote of five to four, that there is no constitutional right to DNA testing after a trial is over. Owen argues that his client's case is different from the one the Supreme Court examined last year. He also cites as a cautionary tale the 2004 execution of Todd Willingham. Willingham was executed by lethal injection, but since then serious questions have been raised about the reliability of the evidence presented against him.