The Moira Jones murder trial has heard how a convicted sex offender admitted he killed the businesswoman in Glasgow's Queen's Park last May.
The accused, Marek Harcar, blames Jason Mulheron for the murder. But the trial heard on Monday that evidence shows he could not have been the killer.
Jason Mulheron told his ex-girlfriend: "It was me, I done the murder of that lassie in the park."
The body of Ms Jones, 40, was discovered by a park ranger. Mr Harcar, a 33-year-old Slovakian national, is standing trial for her rape and murder but denies the charges against him.
He has entered special defences of alibi and incrimination, claiming Mulheron and two other men killed the sales adviser.
Mulheron, 37, has admitted carrying out a serious sex attack not far from where Ms Jones's body was found in Glasgow around two months earlier. He has also admitted being high on a cocktail of drink and drugs on the night the crime was committed.
But Mulheron told the Glasgow High Court he denied claims he had told his former partner about being linked to Ms Jones's death.
He told the court: "I did not confess to it."
The court heard of a conversation Mulheron had with his ex-girlfriend in June 2008.
Paul McBride QC, defending Mr Harcar, asked Mulheron: "Did you say this: 'It was me, I done the murder of that lassie in the park ... it was me that stabbed her'?"
"No," he replied.
The court heard Mulheron's former partner had been so concerned she had contacted police.
Mulheron agreed with Mr McBride it would be "extraordinary" for someone to say this if it had not happened.
Mr McBride added that the jury may hear in evidence that Mulheron had confessed to the crime.
"They may hear it but I did not confess to it," he said.
Mulheron insisted: "I am telling the truth, I am not a murderer, I did not kill Moira Jones."
He agreed with Lord Advocate Elish Angiolini, prosecuting, that no DNA matching his had been found on Ms Jones's body.
This day marked the end of hearing evidence in the trial. The trial before Lord Bracadale continues on Tuesday when closing speeches will be heard.
