Group III-V compounds are very important as the materials of semiconductor devices. Stable structures of the monolayers of group III-V binary compounds have been discovered by using firstprinciples calculations. The primitive unit cell of the discovered structures is a rectangle, which includes four group-III atoms and four group-V atoms. A group-III atom and its three nearestneighbor group-V atoms are placed on the same plane; however, these connections are not the sp(2) hybridization. The bond angles around the group-V atoms are less than the bond angle of sp(3) hybridization. The discovered structure of GaP is an indirect transition semiconductor, while the discovered structures of GaAs. InP, and InAs are direct transition semiconductors. Therefore, the discovered structures of these compounds have the potential of the materials for semiconductor devices, for example, water splitting photocatalysts. The discovered structures may become the most stable structures of monolayers which consist of other materials. (C) 2015 AIP Publishing LLC.