After forming in 1986 , the band appeared on Zagrebfest 1988 . Their song " Rock Me " won the Eurovision Song Contest 1989 in Switzerland , with a score of 137 points . According to author John Kennedy O'Connor in '' The Eurovision Song Contest &ndash; The Official History '' it was an unexpected win . The band proved sceptics wrong , bringing the first and only victory for Yugoslavia . The contest was organised in Zagreb in 1990 . The group members parted ways in 1991
Eurovision Song Contest 1989
Eurovision Song Contest 1989
Riva (band)