In the context of materials science, texture describes the statistical distribution of grain orientations. It is an important characteristic of the microstructure of polycrystalline films, determining various electrical, magnetic and mechanical properties. Three types of texture component are usually distinguished in thin films: random texture, when grains have no preferred orientation; fibre texture, for which one crystallographic axis of the film is parallel to the substrate normal, while there is a rotational degree of freedom around the fibre axis; and epitaxial alignment (or in-plane texture) on single-crystal substrates, where an in-plane alignment fixes all three axes of the grain with respect to the substrate. Here we report a fourth type of texture--which we call axiotaxy--identified from complex but symmetrical patterns of lines on diffraction pole figures for thin films formed by solid-state reactions. The texture is characterized by the alignment of planes in the film and substrate that share the same d-spacing. This preferred alignment of planes across the interface manifests itself as a fibre texture lying off-normal to the sample surface, with the fibre axis perpendicular to certain planes in the substrate. This texture forms because it results in an interface, which is periodic in one dimension, preserved independently of interfacial curvature. This new type of preferred orientation may be the dominant type of texture for a wide class of materials and crystal structures.