The family of James Hanratty, who was hanged for the A6 murder nearly 50 years ago, is calling for the case to be reviewed again.
Hanratty, a small-time thief, was found guilty in 1962 of murdering scientist Michael Gregsten and shooting his mistress Valerie Storie.
The 25-year-old was hanged two months later for the crime but his family have always protested his innocence.
An appeal eight years ago linked Hanratty's DNA to evidence taken from the scene of the 1961 murder in Deadman's Hill on the A6 near Clophill, Bedfordshire. But members of his family say it could have been contaminated and want the Criminal Cases Review Commission to order a fresh review of the evidence.
Hanratty's brother Michael told BBC Radio 4's Today programme: "Jimmy didn't do that (murder Mr Gregsten). I can assure you that, 100%, 120%. He never hurt a soul.
"The day before the execution, his last words were 'Mick, I am completely innocent. Look after mum and dad. Keep an eye on the newspapers, this in years to come will come out'."
The case is being supported by former Private Eye editor Richard Ingrams, who investigated the case with journalist Paul Foot. Mr Ingrams, now at the helm at The Oldie magazine, said he thought the verdict was a "basic case of injustice".
Mr Ingrams said: "It is one of those murder stories that is rather fascinating because it is such an improbable story but I lived with it for many years at Private Eye."
Sir Geoffrey Bindman, the family's solicitor, said: "There's a difference between whether DNA is infallible and reliable and what the evidence is that the particular substance from which the DNA was taken is linked to the crime. That's where the doubts arise and they can arise from different ways if the DNA isn't tested properly - the tests maybe defective, there may be contamination. There are a number of ways you can undermine DNA evidence."