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The reduction of the number of associate classes of some hypercubic association schemes by clubbing certain associate classes has been studied in the paper. It has been found that the reduction of an mclass hypercubic association scheme for v=2 ~ treatments into a 2-class association scheme is always possible. Further it is proved herein that the m-class hypercubic association scheme for v=s ~ treatments is reducible (i) to a 3-class association scheme, when s=3 and (ii) to a 2-class association scheme, when s=4, which really has p'll=p~, and hence leads to a series of balanced incomplete block designs.