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This paper presents a new approach to incorporate in an approximate manner field flux decay into transient stability analysis of multimachine power systems by the second method of Lyapunov; this has not been successful so far in other investigations. In this approach, changes in field flux linkages are not dealt with as other state variables, but treated as parameter variations, because of their small changes, in the conventional stability analysis under the assumption of constant field flux linkages. Therefore, the approach can utilize any Lyapunov function which has been proved to be effective for multimachine power systems, and hence never requires the laborious and very difficult process of constructing an effective Lyapunov function with inclusion of field flux decay. Simulation results have demonstrated the proposed method's practicability and its clear advantage over the exact treatment of the field flux decay attempted by other authors for a simple one machine connected to an infinite bus system.