  We examine the pion exchange mode of neutrinoless double beta decay induced
by the R-parity violating quark-lepton operators of the supersymmetric (SUSY)
extensions of the standard model of the electroweak interactions. The
corresponding nuclear matrix elements are evaluated within the renormalized
quasiparticle random phase approximation with proton-neutron pairing, which
includes the Pauli effect of fermion pairs and does not collapse for a physical
value of the nuclear force strength. It is argued that the pion-exchange mode
of neutrinoless double beta decay dominates over the conventional two-nucleon
mode in the case of the SUSY mechanism. As a result sensitivity of neutrinoless
double beta decay to the SUSY contribution turns out to be significantly better
that previously expected from the two-nucleon mode calculations. An upper limit
on the R-parity violating coupling $\lambda'_{111}$ is derived from
non-observation of neutrinoless double beta decay. This limit is much stronger
than that expected from the near future accelerator experiments.
