  The Schechter-Valle theorem states that a positive observation of
neutrinoless double-beta ($0\nu \beta \beta$) decays implies a finite Majorana
mass term for neutrinos when any unlikely fine-tuning or cancellation is
absent. In this note, we reexamine the quantitative impact of the
Schechter-Valle theorem, and find that current experimental lower limits on the
half-lives of $0\nu \beta \beta$-decaying nuclei have placed a restrictive
upper bound on the Majorana neutrino mass $|\delta m^{ee}_\nu| < 7.43 \times
10^{-29}~{\rm eV}$ radiatively generated at the four-loop level. Furthermore,
we generalize this quantitative analysis of $0\nu \beta \beta$ decays to that
of the lepton-number-violating (LNV) meson decays $M^- \to {M^\prime}^+ +
\ell^-_\alpha + \ell^-_\beta$ (for $\alpha$, $\beta$ = $e$ or $\mu$). Given the
present upper limits on these rare LNV decays, we have derived the loop-induced
Majorana neutrino masses $|\delta m^{ee}_\nu| < 9.7 \times 10^{-18}~{\rm eV}$,
$|\delta m^{e\mu}_\nu| < 1.6 \times 10^{-15}~{\rm eV}$ and $|\delta m^{\mu
\mu}_\nu| < 1.0 \times 10^{-12}~{\rm eV}$ from $K^- \to \pi^+ + e^- + e^-$,
$K^- \to \pi^+ + e^- + \mu^-$ and $K^- \to \pi^+ + \mu^- + \mu^-$,
respectively. A partial list of radiative neutrino masses from the LNV decays
of $D$, $D_s^{}$ and $B$ mesons is also given.
