A major goal in post-genome biology is the complete mapping of the gene regulatory networks for every organism. Identification of regulatory elements is a prerequisite for realizing this ambitious goal. A common problem is finding regulatory patterns in promoters of a group of co-expressed genes, but contemporary methods are challenged by the size and diversity of regulatory regions in higher metazoans. Two key issues are the small amount of information contained in a pattern compared to the large promoter regions and the repetitive characteristics of genomic DNA, which both lead to "pattern drowning". We present a new computational method for identifying transcription factor binding sites in promoters using a discriminatory approach with a large negative set encompassing a significant sample of the promoters from the relevant genome. The sequences are described by a probabilistic model and the most discriminatory motifs are identified by maximizing the probability of the sets given the motif model and prior probabilities of motif occurrences in both sets. Due to the large number of promoters in the negative set, an enhanced suffix array is used to improve speed and performance. Using our method, we demonstrate higher accuracy than the best of contemporary methods, high robustness when extending the length of the input sequences and a strong correlation between our objective function and the correct solution. Using a large background set of real promoters instead of a simplified model leads to higher discriminatory power and markedly reduces the need for repeat masking; a common pre-processing step for other pattern finders.