The 79-year-old was held on Monday on suspicion of murdering 14-year-old Elsie Frost in October 1965.
Elsie was stabbed to death in a tunnel beneath a railway line in Wakefield
The BBC understands the arrested man is Peter Pickering, who was first questioned in connection with the murder in 2016. He was arrested near Newbury, in Berkshire.
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The man is also being questioned in relation to an unconnected allegation of a rape and kidnap in 1972.
Elsie was murdered as she walked home from her school's sailing club, close to the River Calder and the Calder and Hebble Canal.
The West Yorkshire Police Homicide and Major Enquiries team re-opened its investigation into her death after a series of reports on BBC Radio 4.
Mr Pickering was originally arrested in September before being bailed. Police said he had been re-arrested after fresh evidence was uncovered.
The allegations of the 1972 rape and kidnap are understood to have emerged during the course of their investigation into Elsie's death.
A man has been arrested for a second time in connection with the killing of a schoolgirl more than 50 years ago.