In this article we consider optimization problems where the objectives are fuzzy functions (fuzzy-valued functions). For this class of fuzzy optimization problems we discuss the Newton method to find a non-dominated solution. For this purpose, we use the generalized Hukuhara differentiability notion, which is the most general concept of existing differentiability for fuzzy functions. This work improves and corrects the Newton method previously proposed in the literature. (C) 2015 Elsevier B.V. All rights reserved. ; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) ; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)