The construction of a canonical, or normal, representation for non-linear systems, similar to the Morse canonical form in the linear case, is obtained. The problem considered consists, in particular, of studying the existence of generalized transformations that achieve a desired block decoupling. Such transformations generalize the notions of state transformation, state feedback and output injection. A sufficient condition is given in terms of a separability condition, which in turn is completely characterized by using differential forms and their properties.