There are a few algorithms designed to solve the problem of the optimal alignment of one sequence, the pattern, of length m, with another, longer sequence the text, of length n These algorithms allow mismatches, deletions and insertions. Algorithms to date run in 0(mn) time. Let us define an integer. k, which is the maximal number of differences allowed We present a simple algorithm showing that sequences can be optimally aligned in O(k2) time. For long sequences the gain factor over the currently used algorithms is very large.