  An extension of the adjoint SU(5) model with a flavour symmetry based on the
Z_4 group is investigated. The Z_4 symmetry is introduced with the aim of
leading the up- and down-quark mass matrices to the
Nearest-Neighbour-Interaction form. As a consequence of the discrete symmetry
embedded in the SU(5) gauge group, the charged lepton mass matrix also gets the
same form. Within this model, light neutrinos get their masses through type-I,
type-III and one-loop radiative seesaw mechanisms, implemented, respectively,
via a singlet, a triplet and an octet from the adjoint fermionic 24 fields. It
is demonstrated that the neutrino phenomenology forces the introduction of at
least three 24 fermionic multiplets. The symmetry SU(5)xZ_4 allows only two
viable zero textures for the effective neutrino mass matrix. It is showed that
one texture is only compatible with normal hierarchy and the other with
inverted hierarchy in the light neutrino mass spectrum. Finally, it is also
demonstrated that Z_4 freezes out the possibility of proton decay through
exchange of colour Higgs triplets at tree-level.
