Unidirectional propagation of chemical waves in the Belousov-Zhabotinsky (BZ) reaction system was demonstrated using patterns of a BZ catalyst on a cation-exchange membrane, The unidirectional propagation was observed when the chemical waves entered catalyst-less microgaps separating catalyst zones with different thicknesses on the membrane. The chemical waves could pass through the microgaps from a thinner catalyst zone and could not pass through the microgaps from a thicker catalyst zone. The study shows that the asymmetry of excitability of the both zones and the gap width between them are key factors that caused the unidirectional propagation. Computer simulations reproduce the unidirectional propagation.