There is a growing interest in exploiting the functional properties of niobium oxides in general and of the T-Nb2O5 polymorph in particular. Fundamental investigations of the properties of niobium oxides are, however, hindered by the availability of materials with sufficient structural perfection. It is expected that high-quality T-Nb2O5 can be made using heteroepitaxial growth. Here, we investigated the epitaxial growth of T-Nb2O5 on a prototype perovskite oxide, SrTiO3. Even though there exists a reasonable lattice mismatch in one crystallographic direction, these materials have a significant difference in crystal structure: SrTiO3 is cubic, whereas T-Nb2O5 is orthorhombic. It is found that this difference in symmetry results in the formation of domains that have the T-Nb2O5 c-axis aligned with the SrTiO3 <001>s in-plane directions. Hence, the number of domain orientations is four and two for the growth on (100)s- and (110)s-oriented substrates, respectively. Interestingly, the out-of-plane growth direction remains the same for both substrate orientations, suggesting a weak interfacial coupling between the two materials. Despite challenges associated with the heteroepitaxial growth of T-Nb2O5, the T-Nb2O5 films presented in this paper are a significant improvement in terms of structural quality compared to their polycrystalline counterparts.