Thin-film epitaxy is critical for investigating the original properties of materials. To obtain epitaxial films, careful consideration of the external conditions, i.e. single-crystal substrate, temperature, deposition pressure and fabrication method, is significantly important. In particular, selection of the single-crystal substrate is the first step towards fabrication of a high-quality film. Sapphire (single-crystalline α-Al2O3) is commonly used in industry as a thin-film crystal-growth substrate, and functional thin-film materials deposited on sapphire substrates have found industrial applications. However, while sapphire is a single crystal, two types of atomic planes exist in accordance with step height. Here we discuss the need to consider the lattice mismatch for each of the sapphire atomic layers. Furthermore, through cross-sectional transmission electron microscopy analysis, we demonstrate the uniepitaxial growth of cubic crystalline thin films on bistepped sapphire (0001) substrates.