Abstract: The present segmented-direct-integration method is improved for nonlinear dynamic systems governed by the equation , and new predict formulas are proposed. As a precise integration method with explicit, predict-correct, self-starting and four order accuracy, the improved method is not necessary to differentiate . Numerical examples show that the improved method is suitable for multi-degrees of freedom, strongly nonlinear and non-conservative dynamic systems, even effective in studying stability of solution. Moreover, the improved method has higher accuracy than the present segmented-direct-integration method as well as classical Runge-Kutta integration method.