Haroula Kipouridou was last seen alive in the early hours of July 3, 1981, after a shift at a hotel in Fitzroy in inner-north Melbourne where she worked as a singer.
Two associates had given the 25-year-old Richmond woman a lift home to a housing tower on Elizabeth Street after work.
They dropped her off in front of the building about 2am and did not see anything suspicious at the time.
Ms Kipouridou's body was discovered half an hour later on the floor of the tower's lift. She had been severely physically and sexually assaulted.
Investigators at the time spoke to a large number of people, with homicide officers deeming several people potential suspects.
But police have been unable to determine who the offender or offenders were and no one has been charged over Ms Kipouridou's death.
Victoria Police on Sunday announced a $1 million reward for information to help solve the murder, and the possibility of indemnity from prosecution.
More than 40 years on, detectives have not given up on finding those responsible, Homicide Squad detective inspector Dean Thomas said.
"Haroula's death was nothing short of brutal," he said.
"It involved a significant amount of violence and her last moments would have involved pain and fear."
The reward for information leading to the arrest and conviction of those responsible for Ms Kipouridou's death will be paid at the discretion of the police chief commissioner.
News reports at the time suggested police had focused on one suspect, but the force said there had not been sufficient evidence to conclusively say that person was responsible.
Three months after her death, a $50,000 reward was announced, and authorities hope the renewed appeal will lead someone to come forward with information.
"We know people who commit or are part of horrific crimes such as these will often disclose their actions to someone," Det Insp Thomas said.
"People's circumstances can change over the years and someone who may not have wanted to provide information to police previously may now feel ready to do so."
A coroner in 1983 returned an open finding into Ms Kipouridou's death.
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