Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)The paper considers the problem of phylogenetic tree construction. Our approach to the problem bases itself on a non-parametric paradigm seeking a model-free construction and symmetry on Types I and II errors. Trees are constructed through sequential tests using Hamming distance dissimilarity measures, from internal nodes to the tips. The method presents some novelties. The first, which is an advantage over the traditional methods, is that it is very fast, computationally efficient and feasible to be used for very large data sets. Two other novelties are its capacity to deal directly with multiple sequences per group (and built its statistical properties upon this richer information) and that the best tree will not have a predetermined number of tips, that is, the resulting number of tips will be statistically meaningful. We apply the method in two data sets of DNA sequences, illustrating that it can perform quite well even on very unbalanced designs. Computational complexities are also addressed. Supplemental materials are available online.82912871297Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)