Identification of a transcription factor binding sites is an important aspect of the analysis of genetic regulation. Many programs have been developed for the de novo discovery of a binding motif (collection of binding sites). Recently, a scoring function formulation was derived that allows for the comparison of discovered motifs from different programs [S.T. Jensen, X.S. Liu, Q. Zhou and J.S. Liu (2004) Stat. Sci., 19, 188-204.] A simple program, BioOptimizer, was proposed in [S.T. Jensen and J.S. Liu (2004) Bioinformatics, 20, 1557-1564.] that improved discovered motifs by optimizing a scoring function. However, BioOptimizer is a very simple algorithm that can only make local improvements upon an already discovered motif and so BioOptimizer can only be used in conjunction with other motif-finding software.