  In the type-I seesaw mechanism, both the light Majorana neutrinos (\nu_1,
\nu_2, \nu_3) and the heavy Majorana neutrinos (N_1, ..., N_n) can mediate the
neutrinoless double-beta (0\nu\beta\beta) decay. We point out that the
contribution of \nu_i to this 0\nu\beta\beta process is also dependent on the
masses M_k and the mixing parameters R_{ek} of N_k as a direct consequence of
the exact seesaw relation, and the effective mass term of \nu_i is in most
cases dominant over that of N_i. We obtain a new bound |\sum R^2_{ek} M_k| <
0.23 eV (or < 0.85 eV as a more conservative limit) at the 2\sigma level, which
is much stronger than |\sum R^2_{ek} M^{-1}_k| < 5 \times 10^{-8} GeV^{-1} used
in some literature, from current experimental constraints on the 0\nu\beta\beta
decay. Taking the minimal type-I seesaw scenario for example, we illustrate the
possibility of determining or constraining two heavy Majorana neutrino masses
by using more accurate low-energy data on lepton number violation and
non-unitarity of neutrino mixing.
