Unmanned aerial vehicles and hybrid cars, which are currently being studied extensively, require high effiency and power-to-weight ratio engines. The Pars engine, which is a rotary engine that have the potential to provide these desired characteristics, consisting of compressor, combustion chamber and turbine, is similar to the single vane rotary refrigerant compressors and expanders used in the industry. In this study, a new two-stage turbine was designed in place of the Pars turbine, which has a rotary valve system. Expansion ratio, eccentricity ratio, volume ratio, phase difference angle were determined as design parameters and theoretical moment values were obtained. In the theoretical calculations made, a torque increase of 47% vas obtained for equal inlet time angels relative to the rotary valve system in the two-stage turbine.