  Based on current experimental results, such as neutrino oscillations and the
neutrinoless double beta decays (i.e. data from Super Kamiokande, KamLAND, SNO,
etc.), the neutrino mixing matrix can be adequately determined. Though there
are still certain parameters that have possibility limits, but based on the
current experimental results it is possible to construct a general form of
neutrino mass matrix. Starting from this general form of the neutrino mass
matrix we put certain conditions in the context of the seesaw mechanism model
to determine the possible pattern of the neutrino mass matrix that has a
texture zero. From the obtained neutrino mass matrix pattern, there are three
class of patterns, where two of the class are known to be realized in
literature by the underlying family symmetries of the $D_{4}$ and $A_{4}$
groups, the dihedral and tetrahedral symmetry groups.
