We have observed the configuration and motion of surface steps on the aperiodic icosahedral (i-) Al-Pd-Mn quasicrystal using low-energy electron microscopy and scanning tunneling microscopy. As the quasicrystal is cooled from high temperature, bulk vacancies migrate to the surface causing the surface to be etched. Surprisingly, this etching occurs by two types of steps with different heights moving in different directions with different velocities. The steady-state surface morphology is a uniformly spaced rhomboidal step network. This network requires that the layer stacking near the surface deviates from the bulk quasicrystal stacking.