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Diminutive winger William Rennet was signed by the Bhoys in August 1949 after impressing at junior level with hometown club Perth Celtic.

He made his debut in a 4-0 league defeat at Rangers on September 24th in a match best forgotten by all Celtic followers. He made a total of 15 competitive appearances for the Celts - scoring four goals - but after failing to claim a regular starting place he was released in April 1951. He signed for Arbroath in June that year.