The early morning operation will be carried out at Stonehouse cemetery in Lanarkshire, where John Irvine McInnes was buried in a family grave in 1980. Genetic fingerprinting, carried out on a member of his family, has reportedly established a possible link between him and a woman who was killed in 1969.
Helen Puttock was one of three women murdered after being picked up at Glasgow's Barrowland ballroom in the late 1960s. The murders have long been popularly attributed to a killer, nicknamed "Bible John", because of his reputed habit of quoting heavily from the Bible in conversation.
But some detectives at the time thought more than one man was responsible for the deaths.
A possible DNA link between the dead man and Ms Puttock emerged when forensic scientists checked unsolved murders in Glasgow to see if any evidence could be tested by modern techniques.
They are believed to have tested a semen stain on the clothing of Ms Puttock.
But no such possible evidence is thought to still be in existence in the case of the two other murders, and police have only said they are following "a definite line of inquiry" in the case of Ms Puttock's murder.
Mr McInnes, who is believed to have committed suicide at the age of 41, was buried in 1980 alongside his father.
His mother, who died in 1987 at the age of 91, was buried in the same family grave.
A brother and sister still live in Stonehouse, and his wife at the time was reported yesterday to be now married to a Swedish businessman and living in Saudi Arabia.
Mr McInnes' 31-year-old son lives in Berkshire.Reuse content