HOUSTON (CBSDFW.COM/AP) — A former suburban Houston police officer on death row for hiring a hitman to kill his estranged wife in 1994 is a step closer to execution after he lost an appeal before a federal appeals court.

Prisoner Robert Fratta argued to the 5th U.S. Circuit Court of Appeals that he had new evidence that ballistics tests on a gun he bought excluded it as the murder weapon used to kill his 33-year-old wife, Farah.

Robert Fratta

The challenge was one of five filed to the court by the 61-year-old former Missouri City police officer, who’s been tried and convicted twice for her murder.

The ballistics testing was known to Fratta before his second trial and was offered as evidence but was ruled inadmissible, so it can’t be considered now as new evidence or newly discovered evidence, the appeals court said in a ruling late Tuesday.

“Regardless, even assuming that the ballistics report was ‘new,” that new evidence is not “so strong’ that it undermines our confidence in the jury’s verdict,” the court said in an 11-page opinion.

According to the ballistics report cited in the court ruling, the testing was inconclusive.

Fratta’s first conviction in 1996 was thrown out by a federal judge. He was retried and convicted again in 2009.

In another appeals claim, Fratta contended he should be allowed to file his own appeals even while being represented by an attorney. The Texas Court of Criminal Appeals in 1977 ruled a defendant has no constitutional right to the practice known as hybrid representation, then in 1980 extended its ruling to include appeals.

The 5th Circuit described Fratta’s arguments as “a convoluted theory” that suggested he was unhappy with his appeals lawyers.

The court didn’t rule on three other claims because they were related to the two rejected issues.

Farah Fratta was found shot twice in the head in the garage of her home. Evidence showed her husband had her killed in November 1994 after she filed for divorce and that he tried to collect on her life insurance policy days after her death. Evidence also showed payment for her death was to be $1,000 and a Jeep.

Two other men — Joseph Prystash, the middleman Fratta hired to find someone to do the killing, and triggerman Howard Guidry — also are on death row for her murder.

(© Copyright 2018 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)