In 1937, it was decided to build a new building for the primary department for Buckie Public School immediately opposite the secondary department in West Cathcart Street. The building was, however, too small even before it opened, so classes continued to use the original building in West Church Street into the 1960s. The Banffshire Education Committee decided to make the primary department a separate school in 1969. It was known as Buckie Primary School for a decade until it was renamed Cluny Primary School.