  We reanalyze the Hubbard-I approximation by showing that it is equivalent to
an effective Hamiltonian describing Fermionic charge fluctuations, which can be
solved by Bogoliubov transformation. As the most important correction in the
limit of large U and weak spin correlations we augment this Hamiltonian by
further effective particles, which describe composite objects of a Fermionic
charge fluctuation and a spin-, density- or eta- excitation. The scheme is
valid for positive and negative U. We present results for the single particle
Green's function for the two-dimensional Hubbard model with and without t' and
t'' terms, and compare to Quantum Monte-Carlo (QMC) results for the
paramagnetic phase. The overall agreement is significantly improved over the
conventional Hubbard-I or two-pole approximation.
