Multiple sequence alignment (MSA) is a vital problem in biology. Optimal alignment of multiple sequences becomes impractical even for a modest number of sequences [1] since the general version of the problem is NPhard. Because of the high time complexity of traditional MSA algorithms, even today’s fast computers are not able to solve the problem for large number of sequences. In this paper we present a randomized algorithm to calculate distance matrices which is a major step in many multiple sequence alignment algorithms. The basic idea employed is sampling (along the lines of [2]).