Detectives investigating the murder of student Marsha McDonnell say another incident took place in the same area only an hour before her death.
Marsha was killed just yards from her home
Miss McDonnell, 19, was killed by a blow to her head near her home in Hampton, south west London, in the early hours of 4 February.
Scotland Yard detectives say at about 2315 GMT on 3 February an 18-year-old woman was stalked by a man after she got off a bus in West Molesey - about two miles away from where Miss McDonnell was attacked.
Witnesses and fellow bus passengers are being urged to come forward.
Police say the woman had got off the number 411 bus from Kingston in Walton Road when she saw a man standing nearby.
The man followed her and she became alarmed and changed direction.
At one stage the man began running behind her, but she managed to escape.
The man is described as white, about 5ft 10ins to six feet tall with dark wavy hair, long enough to be tucked behind the ears.
He was unshaven with stubble and wearing a green Parka jacket.
In March, a 16-year-old boy, arrested in connection with the murder of Miss McDonnell, was detained under the Mental Health Act.
Officers investigating Miss McDonnell's death have linked it to two other attacks on teenagers which took place within three miles of where she was killed.
A 17-year-old girl was left with head injuries after being attacked in Walpole Gardens, Strawberry Hill, on 8 January at about 2100 GMT.
She has no memory of being attacked and it was originally assumed she slipped on ice.
An 18-year-old man said he managed to escape unhurt after a hooded attacker had lunged at him with a blunt instrument in Hampton Hill a few weeks after Miss McDonnell's murder.
No one has yet been charged.