We propose a theoretical approach, within the framework of the composite operator method, to include the effects of finite cluster correlations into the self-energy of strongly correlated systems. The Hubbard model is analyzed as significant example. The self-energy is rewritten in terms of two-site composite-operator propagators, which are computed by means of a two-site approximation preserving relevant symmetries (e.g., particle–hole symmetry). The involved composite operators describe charge, spin and pair nearest-neighbor correlations and the excitations related to the induced exchange coupling (J=4t2/U). The procedure results in a very rich band structure going well beyond the results of the two-pole approximation.