A new procedure for the splitting of many-body Hamiltonians into "free" and "interaction" parts is proposed which leads to a rapidly converging perturbation expansion. The efficiency of this method is shown for the case of small molecules : Already first and second order perturbations turn out to produce very reasonable results even for excited states; higher terms rapidly converge to zero. An important point to notice is that our method allows for a priori estimates of the convergence (or divergence) behavior.