Abstract: The method is a direct-time integration method, which is used for the numerical integration of equations of motion in structural dynamics. The equations are second order ordinary differential equations (ODEs). In the viewpoint of differential-algebraic equations (DAEs), motion equations in non-holonomic systems are second order, too. Then method is extended and a new numerical method for the equations of motion in the non-holonomic systems is presented, while the equations are index-2 DAEs. The simulation for a two-wheeled robot by method is carried out，and the method is validated by comparing the solution with DASSL and Radau5. In addition, the numerical experiment also illustrates the second-order accuracy of method for DAEs in non-holonomic systems.