Abstract: The variable structure control (VSC) of discrete time systems is studied in this paper. First of all, the quasi-sliding mode is defined and a detailed physical explanation to it is 'given. Previously established versions of reaching conditions are briefly reviewed and a new and more general version is given: the discrete reaching law. For this new definition of quasi-sliding mode its stability problem is proved meanwhile the linear switching function is determined. The VSC is obtained straightforward by the reaching law method, which is a general design method applicable both to single input and multiple input cases in a simple way.