  We consider a condition for non-degenerate commuting squares of matrix
algebras (finite dimensional von Neumann algebras) called the \emph{span
condition}, which in the case of the $n$-dimensional standard spin models is
shown to be satisfied if and only if $n$ is prime. We prove that the commuting
squares satisfying the span condition are isolated among all commuting squares
(modulo isomorphisms). In particular, they are finiteley many for any fixed
dimension. Also, we give a conceptual proof of previous constructions of
certain one-parameter families of biunitaries.
