HUNTSVILLE, Texas (AP) _ An inmate who claimed he had been wrongly convicted in the 1978 slaying of a security guard during a barroom holdup was executed by injection early today.

Paul Rougeau, a 46-year-old former carpenter from St. Bernard Parish, La., went to his death hours after the U.S. Supreme Court refused a stay of execution.

Three of Rougeau's sisters and a niece filed into the death chamber to watch. ''Love you all,'' he told them. ''Peace be with you all.'' Then he turned to the warden and said he had no final statement.

Rougeau was twice tried and convicted of murdering Albert Wilkins, 50, during a holdup by three men that erupted into a gun battle with police. Witnesses said Rougeau shot Wilkins in the head as the deputy constable moonlighting as a guard pleaded for his life.

Rougeau's younger brother, Joseph, was killed in an exchange of gunfire with police who had pulled up outside the Houston bar. A wounded Rougeau fled but was arrested 12 hours later. A third participant testified against him in a plea bargain.

The holdup men had entered the bar in ski masks, but Rougeau, a frequent customer, was identified by at least two patrons by his voice. His wounds left a trail of blood identified as his.

Rougeau claimed that he nothing to do with the robbery and that he ran out of the bar when the shooting began. He said others pinned the crime on him because he used to hang out there and deal drugs.

''I know in my mind the same that God knows,'' he said in an interview last month. ''My execution won't change the real punishment that's coming in the hereafter for those who think they can get away with this.''

Rougeau contended he was shot the following day at an apartment. Prosecutors said a bullet that could have been used as evidence remained in Rougeau's buttocks, but he denied that and wouldn't let surgeons look for it.

On appeal to the U.S. Supreme Court, Rougeau contended that his lawyers at trial were incompetent and that the Texas death penalty law was unconstitutional.

Rougeau's first conviction was thrown out in 1982 by an appeals court, which ruled that potential jurors were improperly excused for expressing reservations about the death penalty. He was retried the following year.

Rougeau was the 76th prisoner put to death in Texas, and the 236th nationwide, since the Supreme Court in 1976 allowed capital punishment to resume.