A new three step iterative method for solving nonlinear equations is introduced based on the following scheme: Let be an initial guess sufficiently close to a simple root of the equation . The iterative step consists two predictor steps:
and one corrector step:
. The authors show that if the function is sufficiently differentiable on an open interval which contains a single root, and if is sufficiently close to this root, then the proposed iterative algorithm has the fourth-order of convergence. Several numerical examples are given to illustrate the efficiency and performance of the new method.