The Helmert transformation of a set of observations {xj},j= 1, 2, …,Nis applied to give a direct approach to the problem of boundary determination in the case of the χ2-test for location of the normal distribution, i.e. the choice of that set of boundaries which maximizes the power of the test. It is found that no significant increase in power can be achieved by taking a number of classes greater than 20; and even a number as small as 12 is sufficient. Moreover, a power of one-half is achieved for a number of classes much smaller than that required by the Mann-Wald approach. For a preassigned number of classes, symmetrically situated about the origin, it is found that the optimum partition corresponds to equal class-width of about 0.4 standard deviation with pooling of the terminal classes, and this is slightly more powerful than the equal class-probability partition.