  The existing calculations of the nuclear matrix elements of the neutrinoless
double $\beta$-decay differ by about a factor three. This uncertainty prevents
quantitative interpretation of the results of experiments searching for this
process. We suggest here that the observation of the neutrinoless double
$\beta$-decay of {\em several} nuclei could allow to test calculations of the
nuclear matrix elements through the comparison of the ratios of the calculated
lifetimes with experimental data. It is shown that the ratio of the lifetimes
is very sensitive to different models.
