We present a fourth-order finite difference method for general second-order nonlinear boundary value problem $-y''+f(x,y,y')=0$ subject to two-point boundary conditions. We use nonequidistant discretization mesh and each discretization of the differential equation at an interior mesh point is based on just three evaluations of $f$. The present paper extends the results given in Chawla (1978) to the case of nonequidistant mesh. Numerical examples are considered to demonstrate computationally the fourth order of the method.