Barna is 9-time Czechoslovakian champion. His best competitive year was 1992, when he won the European Championship and a bronze medal at the 1992 Winter Olympics. He turned professional after the 1992 World Championship. Professional skating did not agree with him, however. He said, "In amateur skating, it matters how you skate. In professional, it matters how you "dance." And I don’t dance. I liked amateur skating better.". However he did spent close to 10 years as a professional skater. Performing in the most prestigious shows like Champions on Ice tour, World cup tour and many more. As well as competing in World professional competitions, ESPN Legends,Miko Masters and other.
Barna works as a coach now. He has appeared in several television skating programs.