Kidd left Dundee to join Falkirk for the following season, 1986–87. In an ironic twist, Falkirk went to Celtic Park in the penultimate game of the season needing a result to ensure their top-flight status, while Celtic needed to win to retain an outside chance of winning the championship. Kidd came on as a substitute as Falkirk won 2–1, effectively ending Celtic's championship challenge. The winning goal was scored by Jimmy Gilmour. Kidd left Scottish football in 1987 to play for Australian NSL side West Adelaide SC.
