This paper develops an updating algorithm for identifying the parameters of a known structure linear system. As it is known that recursive least squares algorithms are the best for identifying the parameters of time invariant systems. However, in case of having time varying system, the above algorithm can not track the variation in parameters in a good shape. Therefore, two approaches have been developed in the literature to resolve this problem i.e., the forgetting factor approach and the finite window one. This paper unifies the above two approaches in a stable fashion by having an algorithm that contains a variable forgetting factor and a constant window. The effectiveness of the proposed algorithm in tracking the system variable parameters is demonstrated by an example.