  We point out under the assumption of Majorana neutrinos that a lower bound on
the MNS matrix element |U_{e3}|^2 can be derived by using constraint imposed by
neutrinoless double beta decay experiments and by positive detection of
neutrino mass by single beta decay experiments. We show that the lower bound
exists in a narrow region of the ratio of the observables in these two
experiments, <m>_{\beta \beta}/<m>_{\beta}. It means that once the neutrino
mass is detected in the bound-sensitive region one must soon observe signal in
neutrinoless double beta decay experiments.
