Lynne Small, 36, was found murdered in her flat in Addison Grove, Thornliebank, East Renfrewshire on 26 October.
Her body was discovered two days after the disappearance of her neighbour Charles Walker, 52, who was last seen in Main Street, Thornliebank.
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Hide AdHis body was found on 21 November, near Whitecraigs Golf Club in Newton Mearns, East Renfrewshire.
Police said there were no suspicious circumstances surrounding his death.
Strathclyde Police yesterday said that they are not looking for anyone else in connection with Ms Small’s death.