Susan Donoghue was sexually assaulted and killed with a truncheon by an intruder at her home in Bristol on August 5, 1976.
The body of the 44-year-old, who was a night sister at Brentry Hospital, was discovered in her basement flat at 45 Downleaze, Sneyd Park, by her partner.
She had been unwell and had taken the night off from work when she was attacked in bed as she slept.
Ms Donoghue was hit seven times with a truncheon, which was left behind, along with a pair of bloodstained gloves and a tobacco tin.
The summer of 1976 was one of the warmest on record and the murder shocked Bristol, but despite an extensive investigation, the killer was never caught.
However, due to advances in scientific technology, Avon and Somerset Police now have a full DNA profile of the suspect.
This comes months after a similar breakthrough saw Christopher Hampton, aged 64, jailed for life for the rape and murder of 17-year-old Melanie Road in Bath, Somerset, in 1984.
He was caught last year after police matched DNA from Melanie’s clothing to Hampton’s daughter, whose DNA was on the national database after she had been cautioned for criminal damage.
Detective Chief Inspector Julie MacKay, who led the team that brought Hampton to justice, is in charge of the Donoghue investigation.
“As we saw with the Melanie Road case, the passage of time since a murder is no longer an obstacle in securing justice for these victims,” she said.
“The technology used in DNA forensics has come a long way since Susan was murdered and we now have a full DNA profile of the man who sexually abused and murdered her.
“Similarly to the Melanie Road murder investigation, the key to solving this horrific crime is in the painstaking and methodical work my team is undertaking to make sure all the information we have is on the right systems.
“I am convinced that someone out there has information on what happened that August night in 1976.
“I would appeal directly to them, or the killer himself, to come forward now and bring an end to the 40 years of heartache Susan’s family and friends have had to endure.
“Susan was a well-liked and respected woman who was brutally murdered in her own home and I am determined to bring her killer to justice.”
Ms Donoghue grew up as part of a large family in Lisnacrieve, near Fintona, Co Tyrone.
She attended primary school in Fintona and later went to Loreto Grammar School in Omagh.
“Susan was a caring person. She trained as a nurse and liked looking after people,” said Ms MacKay.
“She worked as a ward sister in a hospital looking after vulnerable adults.”
At the time of her death she had an 18-year-old son, who now lives abroad.
“He is really pleased that we are still interested, are still investigating and it still matters, and he takes a lot of hope from that,” the detective said.
“Nothing would make him happier than if we identified the person responsible for killing his mum,” the detective added.