The purpose of the multi-dimension uniformity test is to check whether the underlying probability distribution of a multi-dimensional population differs from the multi-dimensional uniform distribution. The multi-dimensional uniformity test has applications in various fields such as biology, astronomy and computer science. A new test statistic for checking multi-dimensional uniformity was proposed in Chen and Hu (2014). As a special case, the bivariate statistic test is discussed in detail in that paper. The Monte Carlo simulation is used to compare the power of the newly proposed test with the distance-to-boundary test, which is a recently published statistical test for multi-dimensional uniformity. It has been shown that the test proposed in this paper is more powerful than the distance-to-boundary test in some cases. This paper proposes a bivariate distribution with support set [0, 1] × [0, 1]. The proposed distribution can be used as an alternative distribution in power comparison.