At the present time it is often stated that the maximum likelihood or the Bayesian method of phylogenetic construction is more accurate than the neighbor joining (NJ) method. Our computer simulations, however, have shown that the converse is true if we use p distance in the NJ procedure and the criterion of obtaining the true tree (Pc expressed as a percentage) or the combined quantity (c) of a value of Pc and a value of Robinson-Foulds' average topological error index (dT). This c is given by Pc (1 - dT/dTmax) = Pc (m - 3 - dT/2)/(m - 3), where m is the number of taxa used and dTmax is the maximum possible value of dT, which is given by 2(m - 3). This neighbor joining method with p distance (NJp method) will be shown generally to give the best data-fit model. This c takes a value between 0 and 1, and a tree-making method giving a high value of c is considered to be good. Our computer simulations have shown that the NJp method generally gives a better performance than the other methods and therefore this method should be used in general whether the gene is compositional or it contains the mosaic DNA regions or not.