Describing function analysis has been widely adopted in many existing identification methods that are based on relay feedback tests. In these methods, the critical point of the Nyquist curve is usually approximated to the oscillation point. Nevertheless, such an approximation may result in poor accuracy for identification, in particular, for those processes with large dead time. In this paper, we introduce the concept of phase deviation to compensate for the span between the critical point and the oscillation point, so that the ultimate gain and ultimate frequency can be accurately obtained using only a single relay feedback test. The phase deviation is then analytically derived, with which all the model parameters can be identified without any prior information of the dead time or static gain. Numerical examples are given to illustrate the proposed method.