In this paper new implicit higher order accuracy (N-IHOA) time integration based on assumption of constant time step is presented for dynamic analysis. This method belongs to the category of the multi time step integrations. Here, current displacement and velocity are assumed to be functions of the velocities and accelerations of several previous time steps, respectively. This definition causes that only one set of weighted factors appears in the proposed method which lead to the simple approach and reduce the computational efforts. To achieve this purpose, the Taylor series expansion and the Routh-Hurwitz criterion are utilized to verify the accuracy and stability of the proposed integration, respectively. Moreover, some dynamic systems such as the nonlinear vibration, the portal frame and the elastic pendulum will be analyzed to clarify the ability and the efficiency of the proposed time integration. Results show that by a similar time step, the N-IHOA method has more accuracy compared with the common approaches such as Wilson-θ and Newmark-β.