In this paper, we present a single to independent two-phase matrix converter (iS2MC) consisting of eight Gallium Nitride (GaN) based monolithic bidirectional switches for the first time. The modulation algorithm for the switches in the iS2MC was designed more easily than that in the three-phase matrix converter. So far, common emitter back-to-back Insulated Gate Bipolar Transistor (IGBT) configuration was used for one bidirectional switch in the conventional iS2MC to drive a symmetric two-phase induction motor. The GaN based bidirectional switches have high breakdown voltage and low specific on-state resistance. The experimental results show that the power conversion efficiency of the GaN-based iS2MC is higher than that of the IGBT-based iS2MC for all the conditions and 7.2 % higher at maximum.