Rezková discovered athletics through ballet and gymnastics. At the preliminary nominations for the Olympics in Mexico at first she wasn’t accepted. Fortunately, when she competed in the Republic Championship, held in Jablonec nad Nisou, she beat Maria Faithová and Jaroslava Valentová with a new Czechoslovakian record of 182 cm, it all suddenly changed.
At the Olympic Games Rezková jumped 174 cm for only the second time around. But later on, after she shook off the stage fright, she found herself competing for medals with only three other competitors. These were the German Rita Schmid, representing the Soviet Union were Okoroková and Kozyrová. Rezková, Out of them she was the only one who exceeded the height of 182 cm.
After the Olympic Games in Mexico she had to attend all sorts of social events and conferences. Journalists were constantly asking for interviews and as a result preparations for the following European championship were rather chaotic. Despite all that, Rezková excelled herself brilliantly and went on to win the competition.