Exponential　stability　analysis　of　discrete-time　nonlinear　systems　with　a　time-varying　delay　is　concerned　in　this　article.　The　main　contribution　of　this　article　lies　in　proposing　an　improved　stability　analysis　method　called　a　delay-mode-based　functional　method.　The　improved　method　is　presented　by　weakening　a　condition　in　the　Lyapunov-Krasovskii　functional　method.　With　the　help　of　the　new　method,　less　conservative　exponential　stability　criteria　of　discrete-time　linear　systems　with　a　time-varying　delay　are　obtained　and　two　classical　examples　are　given　to　show　that　the　delay-mode-based　functional　method　is　effective.