The paper presents a new bias-compensating least-squares (BCLS) method which can eliminate the noise induced estimation bias even without modelling the noise. By employing a composited signal in the parameter estimation, two estimates for the same part of the system parameter are obtained so that the noise induced bias can be extracted from the difference between these two estimates. With the bias removed, the consistent parameter estimate is obtained. It is shown in the paper that the BCLS method is a member of the class of weighted-instrumental-variable methods. Therefore, the BCLS method also provides a particular way to construct instrumental variables for the identification of a general system.