  It is known that there are infinitely many singularities of multiple zeta
functions and the special values at non-positive integer points are
indeterminate. In order to give a suitable rigorous meaning of the special
values there, Furusho, Komori, Matsumoto and Tsumura introduced desingularized
values by using their desingularization method to resolve all singularities. On
the other hand, Ebrahimi-Fard, Manchon and Singer introduced renormalized
values by the renormalization method \`{a} la Connes and Kreimer and they
showed that the values fulfill the shuffle-type product formula. In this paper,
we show the shuffle-type product formulae for desingularized values.
