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In this paper, we present a new and interesting optimal scheme of order eight in a general way for solving nonlinear equations, numerically. The construction of the scheme is

based on rational function approach. The beauty of the proposed is that it is capable to produce further new and interesting optimal schemes of order eight from every existing

optimal fourth-order scheme whose first substep employs Newton's method. The theoretical and computational

properties of the proposed scheme are fully investigated along with

main theorem which establishes the order of convergence and

asymptotic error constant. Several numerical examples are given

and analyzed in detail to demonstrate faster convergence and high

computational efficiency of the proposed methods.