We report progress in growing non-polar a-plane III-nitride films and heterostructures over a-plane 4H-SiC. a-plane SiC is more closely lattice-matched to a-plane GaN than is r-plane sapphire. Consequently, better structural quality a-plane nitride films may result over a-plane SiC substrates. By migration enhanced metalorganic chemical vapor deposition (MEMOCVD), an atomically smooth (1120)AlN layer with RMS roughness of 0.3nm was obtained. From the results of XRD, the structural defects in the AlN layer on SiC substrates were strongly reduced compared to those grown on r-plane sapphire. Also by applying our selective area lateral epitaxy (SALE) growth procedure, we achieved high structural and optical quality a-plane GaN films on 4H-SiC with RMS roughness only 0.4nm. Therefore, non-polar III-nitride films and heterostructures on SiC substrates are promising building blocks for realizing high performance polarization-free devices.