Insulated AC/DC converters using matrix converters (MCs) have higher efficiency, smaller size, and longer lifespan compared with conventional ones. For downsizing of high-frequency (HF) transformers in these converters, developments of HF output MC control methods are active. It is expected to improve efficiency by applying soft switching techniques for these converters. However, to achieve soft switching, phase difference between an output voltage and a current is required. As a result, output power factor decreases. In this paper, a relationship between soft switching conditions and output power factor is revealed. Considering this relationship, the authors propose a new MC control method to achieve soft switching and maximum output power factor. Additionally, this method enables to suppress the distortion of input currents and reduce ripple of the output current. Also, the MC can control the output current and instantaneous reactive power. The authors confirm that experimental results show validity of the method.