This paper demonstrates a method of using a matrix converter with reverse blocking IGBTs (RB-IGBTs) to drive a brushless DC (BLDC) motor with nonsinusoidal flux distribution. The output currents are nearly rectangular and the input currents are sinusoidal. Recently introduced RB-IGBT modules allow for an efficient implementation of the classical topology 18-switch matrix converter. The RB-IGBT modules are controlled so as to provide the required freewheeling paths for the motor currents. The paper presents a suitable carrier-based modulation strategy along with a discussion of selected design issues. Computer simulation and preliminary experimental results are presented. Major advantages and disadvantages of the system are discussed.