  Let E,F be algebraic vector bundles on a projective algebraic variety. Let
G=Aut(E)XAut(F), acting on W=Hom(E,F). In this paper new methods of
construction of algebraic quotients of open G-invariant subsets of W are
studied. This is done by associating to W a new space of morphisms
W'=Hom(E',F') (with group G'=Aut(E')XAut(F')) in such a way that there is a
natural bijection between the set of G-orbits of an open subset of W and the
set of G'-orbits of an open subset of W'. We can then apply already known
construction methods to G'-invariant open subsets of W' and deduce with the
correspondance new quotients of open G-invariant subsets of W. This is a new
version and a continuation of an older paper.
