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In this paper we propose a very fast randomized heuristic algorithm for multiple sequence alignment (MSA) that is memory efficient and is capable of aligning 8000 sequences of average length 500 under 1 minute on a PC. From the MSA, a fast algorithm for the construction of a phylogenetic tree is also presented, using the concepts of aligned blocks and neighbour-joining, which produces the tree in 40 seconds for the aforesaid alignment. Results of testing our algorithm for different sequence lengths are also tabulated.