This paper proposes a deadzone estimator for robust system identification. In order to cope with the drift phenomena occurred in where system inputs are not sufficiently excited in adaptive control, we introduce a novel and flexible bound condition against a fixed constant. It is derived from a forgetting factor and a rational value of the traces of the covariance matrices between step k and k-1. The key feature of this is that it does not require a priori for the bound. Also, the calculation of it is more simple than the one of literatures. The simulation results are examined for showing the practical performance of this algorithm.