MANN and WALD [3] have given, for the first time, a formula for the choice of the optimal numberkof equi-probable class intervals for thex2-test.This formula leads to relatively highkfor different numbers of the sample size. For the determination ofkthey used the supremum norm in the space of distribution functions as distance notion.BEIER-KÜchler and NEUMANN [5] have improved these results and they found out thatkcan be reduced. In our paper a different norm in the space of distribution functions was used and the results are in good agreement with those of BEIER-KÜchler and NEUMANN.