This paper presents a new switching strategy for 3-phase to 2-phase AC/AC conversions based on matrix converters topologies. The proposed converter is alternative solution for Scott and Le Blanc connections. The control strategy is based on Least Mean Square Errors (LMSE) between the measured and the desired output voltages. By this method, the output voltages have no limitation on the output frequency. Also, the harmonic content of the output voltage is significantly less than the other classical kind of the matrix converters. The most important and valuable characteristic of this new algorithm is that even under unbalanced and significantly distorted input voltage waveforms, the output waveforms turn out to be reasonably clean and balanced. The suggested converter results in reduction of losses, installation area and costs. The proposed converter has been modeled and the simulation results have been compared with experimental results. Good agreement between simulation and measurements indicates the effectiveness of the proposed switching strategy.