A design procedure has been developed to derive the non-dimensional volute geometry in terms of flow area and radius ratio as a function of azimuth angle. This design procedure is based on a specification of the desired rotor inlet conditions in terms of the magnitude and direction of the absolute Mach number. The volute inlet Mach number and flow angle are first selected on the basis of the overall radius ratio of the volute. A uniform acceleration of Mach number with azimuth angle is then assumed in order to develop the non-dimensional design of the volute. The design objectives of a turbine volute are to accelerate the working fluid to the rotor and impart a desired magnitude of angular momentum, to distribute the working fluid uniformly around the rotor periphery, and to meet these objectives with a minimum loss in stagnation pressure. The volute tested has broadly met these objectives. The loss in stagnation pressure is small and the Mach number increases smoothly through the volute passage. The flow distribution around the rotor periphery was satisfactory except for the distribution of flow angle and hence angular momentum.