In this paper, we consider the problem of extracting multiple unordered short motifs in upstream regions of given genes. Multiple unordered short motifs can be considered as a set of short motifs, say M={m₁,m₂,…,m_k}. For a gene g, if each of the motifs m₁,…,m_k occurs in either the upstream region or its complement of g, the gene g is said to be consistent with M. We have developed a fast method to exhaustively search collections of short motifs over given short motifs for a particular set of genes, and rank collections with using multiple objective functions. This method is implemented by employing bit operations in the process of matching short motifs with upstream regions, and identifying the members of genes which are consistent with short motifs. On various putatively co-regulated genes of Sacchromyces cerevisiae, determined by gene expression profiles, our computational experiments show biologically interesting results.