AbstractComplex principal components analysis has been shown to be a useful tool for exhibiting propagating features in spatial‐temporal data sets. As in other applications of principal components analysis, rotation may lead to more interpretable components. Real orthogonal matrices have been used elsewhere, in combination with the varimax criterion, to find rotated solutions, but these fail to show invariance to complex scalings of the initial eigenvectors. It is shown that complex orthogonal, or unitary matrices have the desired invariance, and their use is illustrated on two examples, one synthetic and one involving sea‐level pressure data.