  We present a new computation of the Lepton Flavor Violating effective vertex
involving the Higgs boson and two leptons with different flavors. This vertex
is generated from the integration to one-loop level of the heavy right handed
neutrinos which are considered here within the context of the Low Scale Seesaw
Models and with masses close to the TeV scale. We apply the Mass Insertion
Approximation technique to compute the loop contributions from these heavy
$\nu_R$ and derive a symple analytical formula for the $Hl_il_j$ effective
vertex in terms of the input $Y_\nu$ Yukawa coupling matrix and right handed
$M_R$ neutrino masses. Some interesting phenomenological applications of this
$Hl_il_j$ effective vertex are also included.
