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The computation of the unstable equilibrium point (UEP) is a key step involved in the direct methods of power system transient stability analysis. A new continuation-based method to compute the UEPs is proposed. The mechanical powers of the generators are changed to form a parameterized equation. Then the solution curve of the equation is traced by the continuation method from the stable equilibrium point to a UEP. The direction of power increase is determined to get a UEP relevant to the fault. The obtained UEPs are mostly type-1 and the method is applicable to detailed generator models. The method is tested in several systems and satisfactory results are obtained.