  The electric dipole moments (EDMs) of charged leptons are significantly
suppressed in standard model. It has been found previously that they are even
more severely suppressed in seesaw type models by powers of tiny neutrino
masses as far as a leptonic CP source is concerned. We investigate whether a
Majorana-type Yukawa coupling between charged leptons and a doubly charged
scalar can contribute significantly to their EDMs. An observable EDM would then
help unravel the Majorana nature of neutrinos by a lepton number conserving
quantity. We find that the EDMs are indeed parametrically large, of the form
d_\alpha\propto em_\alpha(m^2_\beta-m^2_\gamma)/m^4 up to logarithms, where
m_\alpha and m are respectively the masses of charged leptons and the scalar.
And they satisfy a sum rule to good precision,
d_e/m_e+d_\mu/m_\mu+d_\tau/m_\tau=0. With the most stringent constraints from
lepton flavor violating transitions taken into account, their values are still
much larger than the mentioned previous results. Unfortunately, even in the
most optimistic case the electron EDM is about three orders of magnitude below
the foreseeable experimental sensitivity.
