  In this paper, using the Atiyah-Ward equivalence and a theorem of Hitchin,
one makes to correspond to certain bundles on the projective space, which are
extensions of instanton bundles (in particular, these new bundles may have the
first Chern class not congruent to 0 modulo the rank), bundles on the
grassmanian Gr(2,4) or on the sphere S4, equiped with certain connections
constructed from data associated to the bundle. Monads for these extensions are
described.
