Compositional data refer to non-negative vectors whose sum is constant and convey relative information. Aitchison (1992) developed a set of criteria for a suitable measure of distance or dissimilarity for compositional data. Based on these criteria, Aitchison (1992) introduced a distance measure for compositional data, known as Aitchison distance. The other published measure, to the best of our knowledge, that satisfies all the criteria is the compositional Kullback-Leibler (C-KL) dissimilarity. This paper introduces a new distance measure for compositional data. The proposed distance measure is capable of handling the zero values in the compositions, unlike Aitchison distance and C-KL dissimilarity. Furthermore, this paper shows that two of the criteria (perturbation invariance and subcompositional dominance) set out by Aitchison (1992) are too stringent for some applications involving compositional data. Two numerical examples from political science are included as counterexamples of perturbation invariance and subcompositional dominance criteria. It has shown that the proposed measure, which does not satisfy both perturbation invariance and subcompositional dominance criteria, perform better than Aitchison distance and C-KL dissimilarity.