A generalization of two modified iterative schemes for solving nonlinear equations suggested by Traub and Ezquerro et al. is presented. This new technique allows to obtain local order of convergence 2 rho + 2 from rho improving the above mentioned results where have been obtained rho+1 and 2 rho+1 from rho respectively. The efficiency is also improved. New numerical algorithms of third and fourth order are used to check the theoretical result given. They are illustrated with numerical examples. (C) 2014 Elsevier Ltd. All rights reserved.