Recently, PArida and Gupta (J. Comp. Appl.Math. 2-6 (2007), 873-877) used Rall's recurrence relations approach (from 1961) to approximate roots of nonlinear equations, by developing several methods, the latest of which is free of second derivative and it is of third order. In this paper, we use an idea of Kou and Li (appl. Math. Comp. 187 (2007), 1027-1032) and modify the approach of Parida and Gupta, obtaining yet another third-order method to approximate a solution of a non-linear equation in a Banach space. We give several applications to our method
