His greatest success was winning the bronze medal at the 1976 Winter Olympics as coach of the German national team He also competed at the 1952 and 1960 Winter Olympics. Unsinn was coach of the German national team on three occasions, 1964, 1975 to 1977 and, again, from 1981 to 1990, coaching the team in 221 internationals.
He died on 4 January 2012.
As a player, he spent most of his career with the EV Füssen, which he won eight national German championships with. As a club coach he also won three German and one Swiss national championships with the Düsseldorfer EG, Berliner South Carolina and South Carolina Bern. He is a member of the IIHF Hall of Fame and has also been awarded the Order of Merit of the Federal Republic of Germany.
