Abstract: Independent Slow Feature Analysis (ISFA) is an algorithm for performing nonlinear blind source separation, which combines linear ICA with Slow Feature Analysis (SFA). In its current form the objective function is based on time-delayed covariance matrices. While the algorithm performs well in general, we occasionally encountered cases in which the estimated sources are highly statistically dependent. Here we present a detailed analysis of these cases, which has revealed that second-order covariance matrices do not guarantee statistical independence of a few signals extracted from a high-dimensional feature space.