Applied Mathematical Sciences, Vol. 6, 2012, no. 93, 4617 - 4625 Fourth-Order Iterative Method Free from Second Derivative for Solving Nonlinear Equations Muhammad Aslam Noor Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad Islamabad, Pakistan noormaslam@hotmail.com Waseem Asghar Khan Department of Mathematics, Institute of Business Management Korangi Creek, Karachi., Pakistan waseemasg@gmail.com Abstract. In this paper, we suggest and analyze a new two-step iterative method without second derivatives for solving nonlinear equations. We prove that the modified method has a fourth-order convergence. The efficiency index of this new method is 4 1/3 = 1.58. Several examples are given to illustrate the efficiency and the performance of the new method. The new two-step iterative method can be considered as an alternative to the present fourth-order convergent methods for solving nonlinear equations. Keywords: Nonlinear equations; Iterative method; Convergence criteria; Numerical examples 1. Introduction It is well known that a wide class of problems, which arise in various discipline of pure and applied sciences, can be studied or formulated as nonlinear equations. In recent years, several numerical methods have been developed for solving nonlinear equations 0 ) ( = n x f . These methods have been suggested and analyzed by using different