The describing function method is commonly used for the prediction of limit cycles in non-linear systems. This method is based upon the representation of signals by a Fourier series, and assigning a gain to the non-linear component derived from its response to a sinusoidal input, In this paper we show that a different approach is feasible which in some respects is the dual of the describing function method. The signals are analysed into a Walsh scries, and a gain is assigned to the linear component of the system derived from its response to a square, wave. In many instances the method is likely to give more accurate predictions of limit cycling.