For a class of discrete-time systems with multiplicative uncertainties, the design and analysis of robust direct model reference adaptive control (MRAC) with normalized adaptive law are investigated. By reproving the discrete-time conclusions on the L-p an L-2 delta relationship properties between the input and the output, and the swapping Lemmas I and II, establishing the properties of discrete-time adaptive law, defining the normalizing signal, and relating the signal with all the signals in the closed-loop system, the stability and robustness properties of the discrete-time MRAC scheme are analysed rigorously in a systematic fashion as in the continuous-time case.