  In this paper we give another proof of the fact that a random overlap array,
which satisfies the Ghirlanda-Guerra identities and whose elements take values
in a finite set, is ultrametric with probability one. The new proof bypasses
random change of density invariance principles for directing measures of such
arrays and, in addition to the Dobvysh-Sudakov representation, is based only on
elementary algebraic consequences of the Ghirlanda-Guerra identities.
