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In this study, a new reaching law for sliding mode control of discrete time systems is proposed and applied to solve the problem of congestion avoidance in multi-source, connection oriented data transmission networks. Since the proposed reaching law does not require switching of the sliding variable between positive and negative values in each successive control step, it leads to chattering free operation, does not cause overshoots and helps achieve 100% exploitation of the bottleneck link available bandwidth. Furthermore, the proposed controller always generates bounded data transmission rates. The rates are limited by design parameters and they do not depend on the network initial conditions. The properties of the proposed controller are stated as three theorems, formally proved and verified in a simulation example.