The recently proposed Recursive Inverse (RI) algorithm was shown to have a similar mean-square-error (mse) performance as the Recursive-Least-Squares (RLS) algorithm with reduced complexity. The selection of the forgetting factor has a significant influence on the performance of the RLS algorithm. The value of the forgetting factor leads to a tradeoff between the stability and the tracking ability. In a system identification setting, both the filter length and a leakage phenomenon affect the selection of the forgetting factor. In this paper, we first analytically show that this leakage phenomenon and the filter length have much less influence on the performance of the RI algorithm. Simulation results, in a system identification setting, validate the theoretical results.