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Determination of the critical stability region has been the most time-consuming part in the transient stability analysis by Liapunov's direct method. In power systems this requires the computation of the unstable equilibrium state of the system closest to its postfault stable equilibrium state. Recently some schemes [1,2] have been proposed for the approximate determination of the closest unstable equilibrium state. In this paper an algorithm based on the physical behavior of the power system is presented. This method is pragmatic, exact, more reliable, and computationally faster than the previous ones. Numerical results of the test studies on two different power systems are also included.