  The contribution of the R-parity violating trilinear couplings in the
supersymmetric model to the fermion electric dipole moment is analyzed at the
two-loop level. We show that in general, the Barr-Zee type contribution to the
fermion electric dipole moment with the exchange of W and Z bosons is not small
compared to the currently known photon exchange one with R-parity violating
interactions. We will then give new upper bounds on the imaginary parts of
R-parity violating couplings from the experimental data of the electric dipole
moments of the electron and of the neutron. The effect due to bilinear R-parity
violating couplings, which needs to be investigated separately, is not included
in our analyses.
