The rigorous alignment of multiple protein sequences becomes impractical even with a modest number of sequences, since computer memory and time requirements increase as the product of the lengths of the sequences. We have devised a strategy to approach such an optimal alignment, which modifies the intensive computer storage and time requirements of dynamic programming. Our algorithm randomly divides a group of unaligned sequences into two subgroups, between which an optimal alignment is then obtained by a Needleman-Wunsch style of algorithm. Our algorithm uses a matrix with dimensions corresponding to the lengths of the two aligned sequence subgroups. The pairwise alignment process is repeated using different random divisions of the whole group into two subgroups. Compared with the rigorous approach of solving the n-dimensional lattice by dynamic programming, our iterative algorithm results in alignments that match or are close to the optimal solution, on a limited set of test problems. We have implemented this algorithm in a computer program that runs on the IBM PC class of machines, together with a user-friendly environment for interactively selecting sequences or groups of sequences to be aligned either simultaneously or progressively.