The problem of finding unknown motifs in DNA sequences has been studied seriously in last three decades and a variety of solution approaches have appeared in the literature. We present an efficient combinatorial approach of finding the optimum motif(s) with the maximum accuracy based on a couple of hash based heuristics, which greatly reduce the searching space and unnecessary computations used in the traditional tree based branch and bound mechanism. The proposed approach was tested for performance with various sized real world datasets and our experimental results showed that the proposed approach achieved the maximum accuracy within the practical time, even better than some popularly used approximate and suffix tree based approaches in most of the cases we tested in our practice.