In this paper, a new technique of homotopy analysis method (nHAM) is proposed for solving
second order nonlinear differential equations. This method improves the convergence of the
series solution, eliminates the unneeded terms and reduces time consuming in the standard
homotopy analysis method (HAM). The proposed provides an approximate solution by
rewriting the second order nonlinear differential equation in the form of two first order dif-
ferential equations. The solution of these two differential equations is obtained as a power
series solution. This scheme is tested on four non-linear exactly solvable differential equa-
tions. Three of the examples are initial value problems and the fourth is boundary value
problem. The results demonstrate reliability and efficiency of the algorithm developed.