  We show that Nearest-Neighbour Interaction (NNI) textures for the quark mass
matrices can be obtained through the introduction of an Abelian flavour
symmetry. The minimal realisation requires a Z_4 symmetry in the context of a
two Higgs doublet model. It is further shown that the NNI textures can be in
agreement with all present experimental data on quark masses and mixings,
provided one allows for deviations of Hermiticity in the quark mass matrices at
the 20% level.
