The grain-by-grain orientation relationships between an Fe2O3 film, grown using pulsed laser deposition, and a polycrystalline SrTiO3 substrate were determined using electron backscatter diffraction. This high-throughput investigation, we call combinatorial substrate epitaxy, enables the characterization of film growth on all grain orientations in a single experiment, allowing the determination of the preferred epitaxial orientation (PEO) of this non-isostructural film/substrate pair. Heavily-twinned rhombohedral alpha-Fe2O3 (hematite) grew epitaxially over the entire orientation space of the cubic perovskite substrate. Over 500 local orientation relationships (ORs) were investigated and more than 90% of these ORs, regardless of the interface plane normal, could be described using a single epitaxial OR: (0001) [10 (1) over bar0](Fe2O3)vertical bar vertical bar (111) [1 (1) over bar0](SrTiO3) . This OR aligns the eutactic (nearly close-packed) planes and directions between these dissimilar crystal structures. Importantly, the growth of Fe2O3 on a single crystalline (100)-SrTiO3 results in several different orientation relationships. These results suggest that growth on high Miller-index (low-symmetry) surfaces provides more general information about the PEO than growth on low Miller-index (high-symmetry) surfaces. The epitaxial film growth on high Miller-index surfaces and the overwhelming observation of the eutaxial OR support the hypothesis that a very small number of simple crystallographic descriptors guide epitaxial film growth over all of orientation space, even for non-isostructural film/substrate pairs. (C) 2013 Elsevier B. V. All rights reserved.