A statistical method is developed for estimating the standard errors of branch lengths in a phylogenetic tree reconstructed without assuming equal rates of nucleotide substitution among different lineages. This method can be easily used for testing whether the length of an interior branch in a reconstructed tree is positive, i.e., whether the topology of the tree is correct. Computer simulations indicate that this method is appropriate for a statistical test. As an example, this method is applied to phylogenetic trees reconstructed for the four hominoid species: human, chimpanzee, gorilla, and orangutan. The results obtained show that the present method provides a powerful statistical test.