By neglecting viscosity, heat conduction and diffusion, a method for investigating the effect of dissociaion on the two dimensional flow of a high temperature supersonic gas stream has been examined. The ideal ‘oxygen-like’ gas introduced by Lighthill (1957) has been used and in all cases the internal modes of the molecules are assumed to be instantaneously adjusted to be in equilibrium with each other. A brief introduction to the ideal dissociating gas and the rate equation is given and then the partial differential equations governing the motion of this ideal gas are treated by a standard characteristic method. Due to the entropy production associated with the chemical reactions, analytical solutions are not possible, and a numerical step-by-step method is used to obtain a solution. As an application of the method developed the flow field around a sharp corner of an ideal dissociating gas is examined and a limited investigation of the free stream conditions and expansion angle on the resulting relaxation zone has been given.