On May 4, 1976, Patricia Columbo, then 19, and Frank De Luca, 39, decided to carry out the plan themselves.
Police questioned Patricia but had no reason to suspect her until the following week.
Columbo has tried and failed to win parole at least 15 times.
Board members voted 10-2 Thursday against granting Columbo parole.
Inspired by the promise of reward money, a friend led police to the men who had discussed killing the Columbo family with Patricia.
After the couple was arrested, De Luca's employees revealed that they had seen him washing and burning bloodstained clothes on the day after the murders.