Based on a new way to compute check points, this paper presents a "Block Recursive" sequence alignment algorithm, which can run in a time requirement between 1.5 mn and 3 mn in general cases but between 1.5 mn and 2 mn for sequences with high similarities. Still, the algorithm keeps a linear space requirement and always guarantees an optimal alignment result. Some experiments show that it runs at least 10% faster than the Hirschberg algorithm if the two compared sequences has a normalized edit distance less than 0.25.