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The present paper deals with a new, computationally efficient, algorithm for Sequential Least Squares (LS) estimation. This scheme requires only O(5p) MAD (Multiplications And Divisions) per recursion to update a Kalman type gain vector; p is the number of estimated parameters. In contrast the well-known fast Kalman algorithm requires O(8p) MAD. The introduced method is the fastest known algorithm featured by the rapid convergence characteristics of exact Least Squares estimation schemes. Another interesting feature of the new algorithm is the balanced role, the forward and backward prediction play.