This　brief　is　concerned　with　the　stability　problem　for　a　class　of　discrete-time　switched　systems　with　unstable　subsystems.　By　constructing　a　quasi-time-dependent　Lyapunov　function,　stability　analysis　criterion　for　nonlinear　switched　systems　is　developed　under　a　designed　switching　rule　in　which　the　fast　and　slow　switching　techniques　are　adopted　for　unstable　and　stable　subsystems,　respectively.　Then,　stability　criteria　for　linear　switched　systems　are　presented.　It　is　shown　that　the　obtained　results　are　more　general　and　less　conservative　than　existing　ones.　Some　comparative　simulations　are　provided　to　demonstrate　the　effectiveness　of　the　proposed　method.