In this article, we propose a new method for computing rare maximal exact matches between multiple sequences. A rare match between k sequences S1; : : :; Sk is a string that occurs at most ti -times in the sequence Si , where the ti > 0 are user-defined thresholds. First, the suffix tree of one of the sequences (the reference sequence) is built, and then the other sequences are matched separately against this suffix tree. Second, the resulting pairwise exact matches are combined to multiple exact matches. A clever implementation of this method yields a very fast and space efficient program. This program can be applied in several comparative genomics tasks, such as the identification of synteny blocks between whole genomes. Key words: alignment, algorithms, strings, suffix trees.