We propose a new reinforcement learning method in the framework of Recursive Least Squares-Temporal Difference (RLS-TD). Instead of using the standard mechanism of eligibility traces (resulting in RLS-TD((Formula presented.))), we propose to use the forgetting factor commonly used in gradient-based or least-square estimation, and we show that it has a similar role as eligibility traces. An instrumental variable perspective is adopted to formulate the new algorithm, referred to as RLS-TD with forgetting factor (RLS-TD-f). An interesting aspect of the proposed algorithm is that it has an interpretation of a minimizer of an appropriate cost function. We test the effectiveness of the algorithm in a Policy Iteration setting, meaning that we aim to improve the performance of an initially stabilizing control policy (over large portion of the state space). We take a cart-pole benchmark and an adaptive cruise control benchmark as experimental platforms.@en