We continue the study of the so-called thematic factorizations of admissible
very badly approximable matrix functions. These factorizations were introduced
by V.V. Peller and N.J. Young for studying superoptimal approximation by
bounded analytic matrix functions. Even though thematic indices associated with
a thematic factorization of an admissible very badly approximable matrix
function are not uniquely determined by the function itself, R.B. Alexeev and
V.V.