Abstract: We discusses the conversion of the one-step Newmark’s method into two-step method and proved that has same order as of one-step method. Next we consider the P-stability and phase properties of the method. We consider the implementation of the method using Newton iteration scheme. Also we discuss the estimation of local error and predictor used and presents the one step of the algorithm and convergence criteria. We discuss the stepsize changing strategy and interpolant used to calculate the back values if required. Finally we present the numerical result by applying the method to solve the stiff nonlinear differential system.