Epitaxial ZnO thin films were prepared on atomically flat sapphire (0001) substrates at various temperatures by laser molecular beam epitaxy. On the as-polished substrates, the in-plane orientation of ZnO thin films was found to be ZnO [10 (1) over bar 0]parallel to sapphire [11 (2) over bar 0] regardless of the deposition conditions. However, films on atomically flat substrates showed two in-plane orientations, ZnO [10 (1) over bar 0]parallel to sapphire [10 (1) over bar 0] and ZnO [10 (1) over bar 0]parallel to sapphire [11 (2) over bar 0], rotated by 30 degrees for films grown at low (400-450 degrees C) and high (800-835 degrees C) temperatures respectively. Ion scattering spectroscopy revealed that the former films were (0001) oriented with the Zn-face forming the topmost surface, whereas the latter films had the (000 (1) over bar) orientation with the O-face at the film surface. This orientation change is discussed by taking thermodynamic stability and growth kinetics into account. The films grown at very high temperature (835 degrees C) showed superior crystallinity even in comparison with bulk single crystals.