  We examine the violation of the Pauli exclusion principle in the
Quasiparticle Random Phase Approximation (QRPA) calculation of the two-neutrino
double beta decay matrix elements, which has its origin in the quasi-boson
approximation. For that purpose we propose a new renormalized QRPA with
proton-neutron pairing method (full-RQRPA) for nuclear structure studies, which
includes ground state correlation beyond the QRPA. This is achieved by using of
renormalized quasi-boson approximation, in which the Pauli exclusion principle
is taken into account more carefully. The full-RQRPA has been applied to
two-neutrino double beta decay of $^{76}Ge$, $^{82}Se$, $^{128}Te$ and
$^{130}Te$. The nuclear matrix elements have been found significantly less
sensitive to the increasing strength of particle-particle interaction in the
physically interesting region in comparison with QRPA results. The strong
differences between the results of both methods indicate that the Pauli
exclusion principle plays an important role in the evaluation of the double
beta decay. The inclusion of the Pauli principle removes the difficulties with
the strong dependence on the particle-particle strength $g_{pp}$ in the QRPA on
the two-neutrino double beta decay.
