This paper shows that the recursive least-squares (RLS) algorithm with forgetting factor is a special case of a varying-coe\$cient model, and a model which can easily be estimated via simple local regression. This observation allows us to formulate a new method which retains the RLS algorithm, but extends the algorithm by including polynomial approximations. Simulation results are provided, which indicates that this new method is superior to the classical RLS method, if the parameter variations are smooth.