  The overall characteristics of the solar and atmospheric neutrino
oscillations are approximately consistent with a tribimaximal form of the
mixing matrix $U$ of the lepton sector. Exact tribimaximal mixing leads to
$\theta_{13}=0$. However, the results from the Daya Bay and RENO experiments
have established, such that in comparison to the other neutrino mixing angles,
$\theta_{13}$ is small. Moreover, the atmospheric and solar mass splitting
differ by two orders of magnitude. These significant differences constitutes
the great enthusiasm and main motivation for our research herein reported.
Keeping the leading behavior of U as tribimaximal. We would make a response to
the following questions: at some level, whether or not the small parameters
such as the solar neutrino mass splitting and $U_{e3}$, which vanish in a new
framework, can be interpreted as a modified FL neutrino mass model?
Subsequently, a minimal single perturbation leads to nonzero values for both of
them? Our minimal perturbation matrix is constructed solely from computing the
third mass eigenstate, using the rules of perturbation theory. Let us point out
that in contrast with~\cite{my}, this matrix is not ad hoc assumed, but is
instead built following a series of steps we will outline. Also in compared to
the original FL neutrino mass model which generalize it by inserting phase
factors, our work is more accurate. Subsequently, we produce the following
results that add new contributions to the literature: a) we obtain a realistic
neutrino mixing matrix with $\delta\neq0$ and $\theta_{23}=45^\circ$; b) the
solar mass splitting term is dominated by an imaginary term, which could induce
the existence of Majorana neutrinos, along with explaining a large CP violation
in nature.
