Scott Singleton, 36, of Broadfield, Crawley, West Sussex told the court that on 4 September 1991 he visited Patricia Reich, his former wife at 11am to see if his daughter had gone to school.
'I made a comment about the kids going off all right. Pat was in a pretty nasty mood, you could cut the air with a knife, so I went and got some car magazines to read,' he said.
Mr Singleton denies murdering Lynne Rogers, 17, of Catford, south-east London, between 4 and 7 of September last year.
She was killed after arranging to meet a man at Charing Cross station who had offered her a job stewarding executive flights with a salary of pounds 14,000.
Five days later Miss Rogers' body was discovered in brambles off a country lane in Rotherfield, East Sussex. She had not been sexually assaulted.
Mr Singleton told the court he arranged to spend 4 September with Mrs Reich the previous day because they had argued over Kim Arnold, his girlfriend. 'We had a little two and eight over the lovebites on my neck' he said.
He said that he left Mrs Reich's house in Highgate, north London, at 3pm and then went to a club in King's Cross before returning to Mrs Arnold's home in Catford at 7.30pm.
Robert Seabrook QC, for the prosecution, said that Mr Singleton had changed his alibi. He initially told police he spent the whole day with Mrs Arnold. Mr Singleton agreed. 'It was obviously a mix-up over the dates,' he said. The trial continues today.