  We investigate the effects of disorder in a hybridized two-dimensional
two-band s-wave superconductor model. The situation in which electronic
orbitals form these bands with angular momentum such that the hybridization
$V_{i,j}$ among them is antisymmetric, under inversion symmetry, was taken into
account. The on-site disorder is given by a random impurity potential $W$. We
find that while the random disorder acts to the detriment of superconductivity,
hybridization proceeds favoring it. Accordingly, hybridization plays an
important role in two-band models of superconductivity, in order to hold the
long-range order against the increase of disorder. This makes the present model
eligible to describe real materials, since the hybridization may be induced by
pressure or doping. In addition, the regime from moderate to strong disorder,
reveals that the system is broken into superconductor 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.
