  We introduce a generalized notion of Schwarzenberger bundle on the projective
space. Associated to this more general definition, we give an ad-hoc notion of
jumping subspaces of a Steiner bundle on ${\Bbb P^n}$ (which in rank $n$
coincides with the notion of unstable hyperplane introduced by Vall\`es, Ancona
and Ottaviani). For the set of jumping hyperplanes, we find a sharp bound for
its dimension. We also classify those Steiner bundles whose set of jumping
hyperplanes have maximal dimension and prove that they are generalized
Schwarzenberger bundles.
