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This paper presents a new algorithm for the identification (tracking) of periodically varying systems. When the system coefficients vary rapidly, conventional adaptive estimators such as the least mean squares (LMS) and the weighted least squares (WLS) algorithms become inefficient. Basis function (BF) algorithms have shown superiority over the conventional ones in tracking the parameters of periodically varying systems. Unfortunately, BF estimators are computationally very demanding. A new recursive inverse basis function estimator (RIBF) and its frequency-adaptive version are proposed which provides a significant reduction in the computational complexity and the mean square parameter estimation error without the need for any error correction code.