In this paper we begin by describing two currently used methods for evaluating phylogenetic trees, one proposed by Fitch and Margoliash [5] and the other proposed by Saitou and Nei [7]. Both methods are heuristic in the sense that not all possible trees are tested to ensure that the best solution has been reached. We develop a matrix representation of unrooted binary trees. The problem of evaluating phylogenetic trees is then transformed into the standard linear least squares problem. Then we propose a matrix decomposition method for evaluating phylogenetic trees.