Abstract: In order to obtain a structural dynamic response, a new step-by-step integration method is presented. The step-by-step recursion method is introduced by 3-order Hermite interpolation of nodal displacements and velocities within a local time domain; two different parameters are varied to obtain good stability and accuracy. This method is characterized with self-starting, high precision and no middle computational procedure. The example result comparison with those of Newmark, Wilson, precise integration, shows that this method is accurate and reliable.