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This paper proposes a new algorithm for achieving discrete-time sliding mode for linear multivariable nominal systems using output feedback. The concept of periodic output feedback is used here. It has been shown that, when the output of the system is sampled slower than the input, there exist a discrete-time sliding mode. The method is very general and is applicable to any controllable and observable linear time invariant square system. The magnetic tape position control application is presented to illustrate the proposed method.