  Motivated by the improving sensitivity, $R$, of experiments on $\mu~Ti
\rightarrow e~Ti$ and the enhanced Higgs nucleon interaction, we study this
lepton number violating process induced by Higgs exchange. Taking the possible
sensitivity, $R \simeq 10^{-16}$, we obtain the constraint on the
Higgs-muon-electron vertex, $\kappa_{\mu e}$, to be less than
$2.4\times10^{-7}$ if the masses of the Higgs scalar and $W$ gauge boson are
the same. $\kappa_{\mu e}$ is also calculated for some models.
