We report a study of the problem of consistent parameter estimation in the general case where the measurement noise is unknown and correlated not only with the system output but also with the system input. A new method is presented for eliminating the noise-induced biases in the least-squares (LS) estimates. In the proposed method, two filters are introduced to filter the system input and output signals, respectively, so that an augmented system with some known zeros and poles is obtained. By shifting the space of the parameters to be estimated and using the known zeros and poles of the parameters to be estimated and using the known zeros and poles, a sufficient number of linear constraints are constructed to determine the noise-induced biases. After eliminating the biases in the ordinary LS estimates, consistent estimates of the parameters are obtained. Analysis shows that the results of the proposed method are independent of the noise model used.