ELA, Volume 7, pp. 53-58, July 2000, abstract. A class of inverse M-matrices Reinhard Nabben Nonnegative matrices whose inverses are M-matrices are called inverse M-matrices. It is still an open problem to characterize all inverse M-matrices. In this note a new class of inverse M-matrices is established. This class of nonsymmetric matrices generalizes the class of strictly ultrametric matrices.