  Moving beyond the classical additive and multiplicative approaches, we
present an "exponential" method for perturbative renormalization. Using Dyson's
identity for Green's functions as well as the link between the Faa di Bruno
Hopf algebra and the Hopf algebras of Feynman graphs, its relation to the
composition of formal power series is analyzed. Eventually, we argue that the
new method has several attractive features and encompasses the BPHZ method. The
latter can be seen as a special case of the new procedure for renormalization
scheme maps with the Rota-Baxter property. To our best knowledge, although very
natural from group-theoretical and physical points of view, several ideas
introduced in the present paper seem to be new (besides the exponential method,
let us mention the notions of counterfactors and of order n bare coupling
constants).
