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The crystal structure of scandium oxide films epitaxially grown on α -Al2O3 (0001) under an ultrahigh-vacuum is studied by single-crystal x-ray diffraction. The Sc2O3 film grows in bixbyite phase on the basal (0001) surface of the sapphire substrate with its (111) axis aligned parallel to the substrate normal. In-plane orientation of the film, however, exhibits two distinct growth directions that are defined by the two possible surface orientations of the stepped α -Al2O3 substrate. The atomic structure of the high-quality epitaxial film is fully relaxed and the film has unusual thickness uniformity.