He won six medals at the European Indoor Championships—two gold, three silver and one bronze—and finished fourth at the 1980 Olympic Games and the 1983 World Championships.
His career best jump of 8.30 metres, achieved in July 1985 in Budapest, is the current Hungarian record.
[5] Then, despite jumping even better at the 1981 European Indoor Championships, Szalma only finished fourth with 7.90 metres, eleven centimetres behind the winner Rolf Bernhard.
[12] At the end of the season he finished third at the 1985 World Cup, tying with but losing to Robert Emmiyan at 8.09 metres.
[1] In 1988 he won his last silver medal at the European Indoor Championships, finishing three centimetres behind Frans Maas and three ahead of Giovanni Evangelisti.
He became the Hungarian long jump champion in 1978, 1980, 1981, 1982, 1983, 1985 and 1988, rivalling with Béla Bakosi, Gyula Pálóczi, Zsolt Szabó and Csaba Almási.