Zinc oxide film has a tendency to grow with strong (001) preferential orientation. However, we have reported that the preferential orientation could be changed by changing the gas composition on sputtering. On hetero-epitaxial growth, competition occurs between the preferential and the epitaxial orientation. Then, an investigation as to whether there is a condition which changes the preferential orientation on single crystal substrates (epitaxial growth) and how to obtain excellent epitaxial ZnO films when the preferential orientation is not the same as the epitaxial one was performed. On C-cut sapphire, the (001) textured film was grown under various sputtering conditions. We considered that the worst condition to obtain (001) epitaxial film on the substrate must be the condition to grow without an influence of the self-texture (the preferentially oriented growth caused by the directed orbitals). Under the condition, most excellent (110) and (101) epitaxial films were obtained on R-cut sapphire and (100) MgO, respectively.