  In the present paper we investigate the Gromov--Hausdorff distances between a
bounded metric space $X$ and so called simplex, i.e., a metric space all whose
non-zero distances are the same. In the case when the simplex's cardinality
does not exceed the cardinality of $X$, a new formula for this distance is
obtained. The latter permits to derive an exact formula for the distance
between a simplex and an ultrametric space.
