 Unett began to compete in rallies and in 1977 he took part in the Galway International Rally using Hillman Avenger modified for group 1, finishing 6th overall and winning the team prize with Robin Eyre-Maunsell and Derek McMahon.He also entered the Manx rally (now called the Rally Isle of Man) in an Avenger with Paul White as co-driver, finishing in 6th place with 13021 points.In the same year, Unett was awarded the very first British Racing Drivers' Club 'Silver Star', one of the UK motor sports most prestigious awards.