Summary: In this paper, we propose a new deterministic off-line identification method that obtains a state-space model by using input and output data with steady state values. This method is composed of the method [M. Kosaka, K. Koizumi and H. Shibata, Trans. Soc. Instrument Control Eng. 36, No. 4, 319–327 (2000)] zeroing the \(0 \sim\) \(N\)-tuple integral values of output error of single-input single-output transfer function model and Ho-Kalman’s method [H. P. Zeiger and A. J. McEwen, IEEE Trans. Autom. Control 19, No. 2, 153 (1974; Zbl 0301.93017)]. The feature is that this method can identify by using step responses and, consequently, this is suitable for mechanical system identification in which noise and vibration are undesirable. Numerical simulations of multi-input multi-output system identification and experimental results are illustrated.