  We consider a compact twistor space P and assume that there is a surface S in
P, which has degree one on twistor fibres and contains a twistor fibre F, e.g.
P a LeBrun twistor space. Similar to Donaldson and Buchdahl we examine the
restriction of an instanton bundle V equipped with a fixed trivialisation along
F to a framed vector bundle over (S,F). First we develope inspired by
Huybrechts and Lehn a suitable deformation theory for vector bundles over an
analytic space framed by a vector bundle over a subspace of arbitrary
codimension. In the second section we describe the restriction as a smooth
natural transformation into a fine moduli space. By considering framed
U(r)-instanton bundles as a real structure on framed instanton bundles over P,
we show that the bijection between isomorphism classes of framed U(r)-instanton
bundles and isomorphism classes of framed vector bundles over (S,F) due to
Buchdahl is actually an isomorphism of moduli spaces.
