The development of a rotational inviscid compressible inverse design method for two-dimensional internal flow configurations is described. Rotationality is due to incoming entropy gradient whereas total enthalpy is considered to be constant throughout the flowfield. The method is based on the potential function/stream function formulation. The Ciebsch formulation is adopted to decompose the velocity vector into a potential and a rotational part. The physical space on which the boundaries of the flowfield are sought is mapped onto the (phi, psi) space via a body-fitted coordinate transformation. A novel procedure based on differential geometry arguments is employed to derive the governing equation for the velocity. The velocity equation solved in conjunction with a transport equation for a thermal drift function provide the flowfield without any geometry feedback. An auxiliary orthogonal computational grid adapted to the solution is employed. Geometry is determined by integrating Frenet equations of the grid lines. Inverse calculation results are compared with results of direct ''reproduction'' calculations.