This note by Murray Rosenblatt discusses a transformation that converts an absolutely continuous $k$-variate distribution $F(x_1, \cdots, x_k)$ into a uniform distribution on the $k$-dimensional hypercube. The transformation is defined by a series of cumulative distribution functions, and it is shown that the transformed random vector $Z = TX$ is uniformly distributed on the hypercube. This transformation is useful for setting up regions of equal probability mass in chi-square tests of goodness of fit and for testing the Kolmogorov-Smirnov and von Mises statistics for samples from a uniform distribution. The note also provides an explicit form of the transformation for a normal distribution and discusses the implications for various statistical tests.This note by Murray Rosenblatt discusses a transformation that converts an absolutely continuous $k$-variate distribution $F(x_1, \cdots, x_k)$ into a uniform distribution on the $k$-dimensional hypercube. The transformation is defined by a series of cumulative distribution functions, and it is shown that the transformed random vector $Z = TX$ is uniformly distributed on the hypercube. This transformation is useful for setting up regions of equal probability mass in chi-square tests of goodness of fit and for testing the Kolmogorov-Smirnov and von Mises statistics for samples from a uniform distribution. The note also provides an explicit form of the transformation for a normal distribution and discusses the implications for various statistical tests.