  We present an analysis of modulational instability of diffractionless waves
in a face-centered square lattice of waveguides featuring non-Kerr
nonlinearity, which are constituted by a combination of positive and negative
refractive indices. The unit cell of the lattice consists of three different
waveguides with different optical properties. The dispersion curve of the
lattice supports flat bands and thereby the base equations describing the model
have particular solutions that correspond to the diffractionless waves
propagating along the waveguides. We also observe a unique ramification of
nonlinearities in controlling the flat bands optically. The diffractionless
wave solutions are derived and the stability of these distributions are
investigated in a nutshell by adopting the standard linear stability approach.
