  We propose the generalized Friedberg-Lee model neutrino mass model at a
particular point (point D at which $\alpha=\beta=-\frac{1}{3}$) where at this
point, the generalized Fridberg-Lee model is converted to the Democratic mass
matrix with the $S_3$ symmetry. The Democratic texture has an experimentally
unfavored degenerate mass spectrum on the base of the tribimaximal mixing
matrix $(U_{TBM})$. We modify the Democratic mass matrix, at point D, to obtain
a nondegenerate mass spectrum by adding the breaking mass term as preserving
the twisted Fridberg-Lee symmetry. Although the mixing matrix is still
$(U_{TBM})$, where leads to $\theta_{13}=0$ which is not consistent with the
results from Daya Bay and RENO experiments that have established a nonzero
value for $\theta_{13}$.
  preserving the leading behavior of $U$ as tribimaximal, and we apply the
Broken Democratic neutrino mass texture as a mass matrix at point D.
Subsequently, we characterize a minimal perturbation mass matrix which is
responsible for a nonzero $\theta_{13}$ along with CP violation parameters,
besides the solar neutrino mass splitting has been resulted from it. Let us
mention that, unlike other investigations, the perturbation matrix is not
adopted on an ad hoc basis, but is generated only in one step by the rules of
perturbation method that we will describe. Subsequently, we develop the
following results to the literature: (a) we obtain the corresponding neutrino
mixing matrix of the generalized Fridberg-Lee model at point D with
$\theta_{23}=\frac{\pi}{4}$ and non-zero $\delta$; (b) the ordering of the
neutrino masses is inverted; (c) we also obtain the allowed range of the mass
parameters, the Dirac phase and the Jarlskog parameter which are consistence
with the available experimental data.
