In this paper, we proposed a new ARMA model identification which estimate the parameters to make the current prediction error uncorrelated with the past one. As good properties of the proposed method, we show the uniqueness, consistency of the estimate and asymptotic normality of the estimation error. Via simulation results, we show that the proposed method give good estimates for various systems which have different power spectrum. Moreover, the estimation of gyroscope random errors shows that the proposed method is applicable to the real data.