A novel strain mismatch induced tilted epitaxy method has been demonstrated for producing high quality (000l) hexagonal films on (001) cubic substrates. Highly oriented hexagonal (000l) ZnO films are grown on cubic (001) MgO substrates using Sm0.28Zr0.72O2−δ (SZO) as a template. The large lattice mismatch of >13% between the obvious crystallographic matching directions of the template and substrate means that cube-on-cube epitaxy is energetically unfavorable, leading to growth instead of two high index, low energy compact planes, close to the {111} orientation. These planes give three different in-plane orientations resulting from coincidence site lattice matching (12 in-plane orientations in total) and provide a pseudo-hexagonal symmetry surface for the ZnO to grow on. The texture of the ensuing (000l) ZnO layer is markedly improved over the template. The work opens up both a new avenue for growing technologically important hexagonal structures on a range of readily available, (001) cubic substrates, as well as showing that there are wide possibilities for heteroepitaxial growth of a range of dissimilar materials.