The rapid advancement of technology and measurement devices has enabled the recording of a vast array of features pertaining to an object of study. For such high dimensional data, classical, low dimensional multivariate statistical techniques are not applicable. Consequently, the high dimension of modern big data presents challenges not only in its computational aspects but also in statistical theory. As a contribution to this topic, the work that will be presented introduces a novel approach to distributional-free hypothesis testing for high dimensional data. Specifically, it proposes a novel test for the hypothesis problem of whether two high dimensional samples share the same distribution or not.