This study presents a new four-step iterative method for solving nonlinear equations. The method is based on Newton’s method and has order of convergence sixteen. As this method requires four function evaluations and one derivative evaluation at each step, it is optimal in the sense of the Kung and Traub conjecture. In terms of computational cost, this implies that the efficiency index of our method is 5√16 = 1.741. Preliminary numerical results indicate that the algo- rithm is more efficient and performs better than other existing methods. Key words and phrases. Nonlinear equations, four-step methods, effi- ciency index, order of convergence, simple root.
