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Adaptive filtering schemes are subject to different tradeoffs regarding their steady-state misadjustment, speed of convergence, and tracking performance. To alleviate these compromises, a new approach has recently been proposed, in which two filters with complementary capabilities adaptively mix their outputs to get an overall filter of improved performance. Following this approach, we propose a new normalized rule for adapting the mixing parameter that controls the combination. The new update rule preserves the good features of the existing scheme and is more robust to changes in the filtering scenario, for instance when the signal-to-noise ratio (SNR) is time varying. The benefits of the normalized scheme are illustrated analytically and with a number of experiments in both stationary and tracking situations.