  We report the results of a calculation of the nuclear matrix element of
neutrinoless double-$\beta$ decay of $^{48}$Ca, carried out taking into account
nucleon-nucleon correlations in both coordinate- and spin-space. Our numerical
results, obtained using nuclear matter correlation functions, suggest that
inclusion of correlations leads to a $\sim$ $20\%$ decrease of the matrix
element, with respect to the shell model prediction. This conclusion is
supported by the results of an independent calculation, in which correlation
effects are taken into account using the spectroscopic factors of $^{48}$Ca
obtained from an {\em ab intitio} many body approach.
