Clyde gained entry into the Friendship Cup in 1960. It was an inter-League competition between four clubs each from England, France and Scotland, with results aggregated to provide the 'best' League. It proved to be an unpopular format and ended in 1962. For the record, Clyde was drawn against RC Lens of France and beat them 4–0 away and 2–1 at Shawfield. The club began the 1960s as a yo-yo club. Relegations in 1960–61 and 1962–63 were followed by immediate promotions in 1961–62 and 1963–64, the former as Division Two champions.