  It is known that the special values of multiple zeta functions at
non-positive arguments are indeterminate in most cases due to the occurrences
of infinitely many singularities. In order to give a suitable rigorous meaning
of the special values there, Furusho, Komori, Matsumoto and Tsumura introduced
the desingularized values by the desingularization method to resolve all
singularities. While, Ebrahimi-Fard, Manchon and Singer introduced the
renormalized values to keep the "shuffle" relation by the renormalization
procedure \`a la Connes and Kreimer. In this paper, we reveal an equivalence,
that is, an explicit interrelationship between these two values. As a
corollary, we also obtain an explicit formula to describe renormalized values
in terms of Bernoulli numbers.
