  We investigate the effects of disorder in a simple model of a hybridized
two-dimensional two-band s-wave superconductor. We take into account the
situations in which these bands are formed by electronic orbitals with angular
momentum such that the hybridization $V(\mathbf{k})$ among them is
antisymmetric, under inversion symmetry. The impurity potential is given by an
independent random variable $W$ which controls the strength of the on-site
disorder. We find that while the random disorder acts in detriment of
superconductivity, hybridization proceeds favoring superconductivity. This
shows that hybridization, which may be induced by pressure or doping, plays an
important hole in two-band models of superconductivity, making them eligible
candidates to describe real materials. We also find that in moderate and strong
disorder, the system is broken into islands, with correlated local order
parameters. These correlations persist to distances of several order lattice
spacing which corresponds to the size of the SC-Islands.
