Normally, when one identifies a system from input-output data in a time domain, it is assumed that the data length is long enough and the autoregressive with exogeneous input (ARX) model order is sufficiently large. In the residual whitening method, one uses the autoregressive moving average with exogeneous input (ARMAX) model which includes the dynamics of noise instead of ARX model to minimize and whiten the residual. The properties of the residual sequence, i.e., the orthogonal conditions, will convert to the optimal properties of the Kalman filter. One can also relax the requirement of the model order to reduce the computation burden, especially for several input and output systems.