Many different methods have been presented for aligning multiple biological sequences. These methods can be classified into three categories: rigorous, tree-based, and iterative. The rigorous method, which always generates the optimal alignment, requires memory space and computation time proportional to the product of the sequence lengths. Even for a modest number of sequences, this method becomes impractical. As a result, the other two methods were introduced. The iterative methods were shown to generate better alignments than the tree-based methods. However, these methods require as much as 100 times longer computation time. A number of days may be required to align a large number of sequences (e.g., over 100 sequences) sequentially. We present a parallel speculative computational method which reduces the computation time of the iterative methods from days to minutes. To evaluate our parallel method, we implemented a speculative computation version of the iterative improvement method of Berger and Munson on an Intel iPSC/860 parallel computer. The empirical results demonstrate that our parallel method obtained a significant speed up in comparison to the sequential method.