Considering transinent stability of an n-machine interconnected power system when a large disturbance lead to a loss of synchronism, a novel distributed coordination control methed is proposed in order to control the rotor angle error to zero. A pairwise decomposition of the model is performed into $n-1$ interconnected subsystems. A distributed coordination controller is designed to guarantee the local stability of subsystems. The stability regions for each disconnected subsystems are estimated. Then, an aggregate model is constructed involving a vector Lyapunov function and the subsystem-region estimates is used to determine the stability of the overall system. A 3-generator example is given to illustate the effectiveness of the proposed method. This judging method can simplifly the complexity of system stability analysis and reduce the computation load.