This paper presents a new computation method for transient stability analysis for electric power systems. Different from existing methods, a minimization problem is formulated for obtaining critical clearing time (CCT). The method is based on the computation of a trajectory on the stability boundary, which is referred to as critical trajectory in this paper. The critical trajectory is defined as the trajectory that starts from a point on a fault-on trajectory and reaches a critical point of losing synchronism. The new proposal includes the critical conditions for synchronism and the unified minimization formulation using a modified trapezoidal formulation for numerical integration. It will be demonstrated that the solution of the minimization problem successfully provides the exact CCT that agrees with the conventional numerical simulation method.