  In the model-independent context, where the neutrino mass matrix is assumed
to be diagonalized by means of a unitary matrix that possess the Tri-Bi-Maximal
(TBM) flavor mixing pattern. We present an analysis where the TBM deviation is
explored by considering different forms, with texture zeros, for the charged
lepton mass matrix. These last mass matrices are classified into equivalent
classes. We are interested in the charged lepton mass matrices with the minimum
free parameter number, $i.e.$ the maximum number of texture zeros, that allows
us to correctly reproduce the reactor mixing angle value. We show a deviation
from the TBM pattern in terms of the charged lepton masses as well as the
theoretical expressions and their parameter space for the mixing angles.
Finally, we present the phenomenological implications of numerical values of
the "Majorana-like" phase factors on the neutrinoless double-beta decay.
