In the summer of 1986, after six seasons with Dinamo Zagreb, Bračun's contract at Maksimir expired. Since he wasn't offered a new one by head coach Ćiro Blažević, the 28-year-old defender principally agreed his transfer to Hajduk Split. However, later on in the summer transfer window veteran defender Luka Peruzović came back to the club, making Bračun's potential move surplus to requirements. Instead, Bračun accepted an offer from Red Star's sporting director Dragan Džajić and moved to Belgrade.[1]