G. Gaeta Poincare' renormalized forms (42K, TeX) ABSTRACT. In Poincar\'e Normal Form theory, one considers a series of transformations generated by homogeneous polynomials obtained as solution of the homological equation; such solutions are unique up to terms in the kernel of the homological operator. Careful consideration of the higher order terms generated by polynomials differing for a term in this kernel leads to the possibility of further reducing the Normal Form expansion of a formal power series, in a completely algorithmic way. The algorithm is also applied to planar vector fields whose linear part has eigenvalues $\la = \pm i$.