Finding the roots of nonlinear algebraic equations is an important problem in science and engineering, later many methods developed for solving nonlinear equations. These methods are given [1-24], in this work, we proposed two new higher order iterative methods. These methods based on the method given by Rafiullah [1], 2016, which is Eighth and Sixteenth-order convergence. The Least square method is used to find the present methods. We verified on a number of examples and numerical results obtained show that the present method is faster than the other methods.