  We consider a scenario with only one sterile neutrino $ N $, negligible
mixing with the active neutrinos $ \nu_{L} $, where its interactions with
ordinary particles could be described in a model independent approach based on
an effective theory. Under such a framwork, we consider the contributions of
the sterile neutrino $N$ to the pure leptonic decays $ M \rightarrow l\nu $ and
$ \nu \overline{\nu} $, and the radiative leptonic decays $ M \rightarrow
l\nu\gamma $ with $M$ denoting the pseudoscalar mesons $ B $, $ D $ and $ K$.
We find that it can produce significant effects on some of these rare decay
processes.
