A former plastic surgeon has finally confessed to killing his wife and throwing her body off a plane, over 35 years after he committed the crime and two decades after he was convicted for it.

Robert Bierenbaum insisted on his innocence even after he was convicted of his wife Gail Katz's murder in 2000 due to circumstantial evidence. During a parole board hearing amid his prison sentence of 20 years to life in December last year, he finally admitted that he had attacked his wife whose body was never found by the police.

In the chilling confession, which was reported by ABC News as part of the network's two-installment 20/20 special airing Friday at 9 p.m., Bierenbaum said he committed the crime because he wanted Katz to stop yelling at him. He confirmed that the prosecutors' case against him that he killed her and then threw her body out of an airplane over the Atlantic Ocean was correct.

"I wanted her to stop yelling at me and I attacked her," he said, adding that he first "strangled" her, then he went flying. "I opened the door and then took her body out of the airplane over the ocean," he said.

The 66-year-old, who committed the crime when he was 30 years old, had originally told police in July 1985 that his wife has been missing ever since she stormed out of their Manhattan apartment following a heated altercation. He said that he assumed she had gone to Central Park to calm down before he reported her as missing.

He added that he had spent much of that day at their apartment, only leaving to visit family and friends. However, the authorities found out several months later that he had driven to a New Jersey airport and piloted a rented plane on a two-hour flight over the Atlantic Ocean within hours of his wife's disappearance. As the victim's body was never found, it took prosecutors two decades to put Bierenbaum to prison on the basis of circumstantial evidence.

Dan Bibb, one of the prosecutors in the case, said that it "shocked everyone" when the convict revealed that he had killed his wife and dumped her body in the precise way in which prosecutors had made the case. Bibb said, "I was like, 'Holy s---, are you kidding me?' I was stunned because I always thought that that day would never come, that he would own up, take responsibility for having killed his wife."

Police crime tape
Police crime tape MARK RALSTON/AFP/Getty Images)