This paper introduces a new algorithm for implementing subband, adaptive filtering using recursive least squares (RLS) with round robin regularization. We show that modern microprocessors with SIMD (Single Instruction, Multiple Data) instructions can now implement RLS for practical problems thereby avoiding the numerical stability issues associated with fast RLS (FRLS). The desired signal may be multichannel as in the stereo, acoustic echo cancellation (AEC) problem where the separate channels of the playback signals are often highly correlated. In this case, the recursive computation of the inverse correlation matrix in RLS will diverge. To avoid this problem, we extend adaptive subband RLS to include round robin regularization. The new, regularized RLS (RRLS) algorithm has been implemented in real-time on a personal computer (PC) for the stereo AEC problem and performs well in typical PC scenarios.