This paper presents a non-Luré type Lyapunov function for the transient stability analysis of multimachine power systems. A systematic procedure for constructing the Lyapunov function which includes a new term which does not appear in the Luré type function is shown. The procedure is essentially based on the generalised Popov criterion developed by Moore and Anderson. The power system model used in this paper consists of synchronous machines interconnected by a lossless transmission system. It is shown that the conventional Luré type functions and energy functions constructed for this model are regarded as particular cases of the result obtained in this paper. The superiority of the proposed Lyapunov function is illustrated by numerical examples.