Elsie Frost, 14, was attacked from behind and stabbed in the back and head as she walked through a railway tunnel just off a canal towpath in Wakefield, West Yorkshire, in October 1965.
The suspect was arrested in September last year and later bailed. He was re-arrested on Monday.
A West Yorkshire Police spokesman said tonight: (Thurs March 9) : "West Yorkshire Police have this evening bailed a 79-year-old man arrested on suspicion of the murder of 14-year-old schoolgirl Elsie Frost.
"The man, who was re-arrested on 6 March, in Newbury, has been bailed back into secure custody."
"Detectives will now submit a file of evidence to the CPS for them to consider on the offences of kidnap, rape and murder."
Senior Investigating Officer, Detective Superintendent Nick Wallen of the Homicide and Major Enquiry Team, said: "Following extensive interviews, we have now bailed a man we arrested earlier this week in connection with the murder of Elsie Frost.
"We have been in dialogue with a dedicated case lawyer from the CPS` Complex Case Unit and we will now be submitting a file of evidence for them to consider charges in respect of kidnap, rape and murder."
On Monday , West Yorkshire Police said: “Following continued inquiries into the murder of 14-year-old Elsie Frost who was discovered stabbed to death in Horbury, Wakefield, West Yorkshire on October 9 1965, West Yorkshire Police have today re-arrested a 79-year-old man on suspicion of her murder.”