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In a number of adaptive filtering applications, non-Wiener effects have been observed for the (normalized) least-mean-square algorithm. These effects can lead to performance improvements over the fixed Wiener filter with the same model structure, and are characterized by dynamic behavior of the adaptive filter weights. Here we investigate whether such non-Wiener effects can also occur in the recursive least squares algorithm, and under which circumstances. Examples show that non-Wiener effects can also occur with the recursive least squares algorithm, in particular when the exponential forgetting factor is small. The latter corresponds to a short memory depth, the need for which one generally associates with tracking of time-varying phenomena.