In this note, we demonstrate direct high-temperature growth of single-crystalline GaN on c-plane ScAlMgO4 substrates by metalorganic chemical vapor deposition, without using low-temperature buffers. We found that a trimethylaluminium preflow was crucial to suppress island growth and to achieve uniform mirror-like Ga-polar GaN layers. The preflow time was found to have a direct impact on the crystalline quality of GaN. We also show that thin GaN layers directly grown at high temperature can be used as buffers for the growth of lattice-matched In0.17Ga0.83N layers on ScAlMgO4. The presented results demonstrate the potential of direct growth of GaN on ScAlMgO4.