In this paper, a new optimal family of iterative methods with sixteenth-order of convergence for solving nonlinear equations is presented and analysed. This new family of iterative methods is obtained in two stages. The first stage is obtained by composing the optimal fourth-order family of iterative methods proposed by King, 1973, with the classical Newton’s method and then approximating the first-appeared derivative in the last step with a new estimation built on a combination of already evaluated function values. This procedure yields a new eighth-order optimal family of iterative methods. The second stage of our derivation is built on composing the obtained family of iterative methods of eighth-order of convergence with the classical Newton’s method again and then approximating the first-appeared derivative in the last step of the resulting family by a new estimation using combination of already evaluated function values. The convergence analyses of both of the new developed families are studied in this paper. To illustrate our theoretical results and to illustrate the efficiency and the accuracy of our new developed families of optimal iterative methods, limited numbers of numerical examples are calculated and compared with the existing methods.