In　this　note,　we　consider　the　asymptotical　stability　of　hybrid　dynamical　systems　(HDSs)　in　the　sense　of　Lyapunov.　Some　necessary　and　sufficient　conditions　are　derived　which　require　only　the　Lyapunov　function　to　be　non-increasing　along　the　sequences　of　time-interval　of　the　active　subsystems.