Despite the scientific and technological importance of removing interface dangling bonds, even an ideal model of a dangling-bond-free interface between GaN and an insulator has not been known. The formation of an atomically thin ordered buffer layer between crystalline GaN and amorphous SiO2 would be a key to synthesize a dangling-bond-free GaN/SiO2 interface. Here, we predict that a silicon oxynitride (Si4O5N3) layer can epitaxially grow on a GaN(0001) surface without creating dangling bonds at the interface. Our ab initio calculations show that the GaN/Si4O5N3 structure is more stable than silicon-oxide-terminated GaN(0001) surfaces. The electronic properties of the GaN/Si4O5N3 structure can be tuned by modifying the chemical components near the interface. We also propose a possible approach to experimentally synthesize the GaN/Si4O5N3 structure.