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This paper describes a parallel implementation of our recently developed algorithm for phylogenetic analysis on the IBM BlueGene/L cluster. This algorithm constructs evolutionary trees for a given set of DNA or protein sequences based on the topological information of every possible quartet trees. Our experimental results showed that it has several advantages over many popular algorithms. By distributing the quartet weights evenly across the processing nodes and making effective use of a fast collective network on the IBM BlueGene/L cluster, we are able to achieve a close to linear speedup even when the number of processors involved in the computation is large.