  We offer a piece of evidence that the problems of finding the number of
mutually unbiased bases (MUB) and mutually orthogonal Latin squares (MOLS)
might not be equivalent. We study a particular procedure which has been shown
to relate the two problems and generates complete sets of MUBs in
power-of-prime dimensions and three MUBs in dimension six. For these cases,
every square from an augmented set of MOLS has a corresponding MUB. We show
that this no longer holds for certain composite dimensions.
