  The algorithm derived in this article, which builds upon the original paper,
takes a holistic view of the handedness of an orthonormal eigenvector matrix so
as to transfer what would have been labeled as a reflection in the original
algorithm into a rotation through a major arc in the new algorithm. In so
doing, the angular wrap-around on the interval {\pi} that exists in the
original is extended to a 2{\pi} interval for primary rotations, which in turn
provides clean directional statistics. The modified algorithm is detailed in
this article and an empirical example is shown. The empirical example is
analyzed in the context of random matrix theory, after which two methods are
discussed to stabilize eigenvector pointing directions as they evolve in time.
The thucyd Python package and source code, reported in the original paper, has
been updated to include the new algorithm and is freely available.
