Many studies have been conducted in the last two decades to search for traces of recent positive selection, and demography is considered as one of the most important confounding factors. To reduce the confounding impact of demography, the coalescent tree topology has been used as a source of information for detecting recent positive selection in a population or a species. Based on the branching pattern of the root, we partition the hypothetical coalescent tree, inferred from a sequence sample, into two subtrees. Positive selection could impose a strong impact on branch length in one of the two subtrees while demography has the same effect on both subtrees. Thus positive selection should be detectable by comparing statistics calculated for the two subtrees. Simulations demonstrate that the proposed test has high power to detect recent positive selection even when DNA polymorphism data from only one locus is available and that it is robust to the confounding impact of demography. One big asset is that all components in the summary statistics (Du) can be computed analytically. Moreover, mis-inference of derived and ancestral alleles should not affect the test and it therefore avoids an annoying problem when detecting recent positive selection.