A new functional integral mapping of a strongly correlated Fermi system to another Fermi system is presented. The strong correlations appear in the new system through momentum- and frequency-dependent coupling constants characterising correlated multi-particle motions, which can be treated perturbatively. The method is well suited to treat Hubbard and Anderson models. For the Hubbard model, the lowest-order term reproduces Hubbard's two-band Green function. Second-order processes leading to spin fluctuations are identified.