This paper introduces a novel motif discovery algorithm based on the use of constraint mechanism and constraint rules. The key idea is to convert sets of similar substrings of the DNA sequences into patterns, as early as possible, using constraint mechanism or constraint rules. The advantages are two folds. Firstly, the approach generates limited number of patterns while still guaranteeing that the actual motifs are contained in the pattern set. Secondly, the procedure for deriving patterns is very cost-effective since it can be considered as that we use many "look ahead" to speed up the procedure. Therefore, the algorithm has the advantages of the high sensitivity of pattern-driven algorithms as well as the efficiency of sample-driven algorithms.