Bandgap energies of the group III-V quaternary alloy semiconductor, cubic Al x Ga1−x N y As1−y , were calculated by means of the dielectric method. While only GaN and GaAs are considered to be direct transition type among the four constituent binary compounds of this quaternary alloy system, the calculation results show that the bandgap energy range covered in the direct transition regime of this alloy system was further extended to the higher energy side of GaN as well as to the lower energy sides of GaAs. The extension to the higher energy side was attributed to the larger direct bandgap of AlN. On the other hand, the extension to the lower energy side was caused by the large bowing in the bandgap energy between group III nitrides and arsenides. Calculations under lattice matching to Si and GaAs are also presented.