  We study in this paper very badly approximable matrix functions on the unit
circle $\T$, i.e., matrix functions $\Phi$ such that the zero function is a
superoptimal approximation of $\Phi$. The purpose of this paper is to obtain a
characterization of the continuous very badly approximable functions.
  Our characterization is more geometric than algebraic characterizations
earlier obtained in \cite{PY} and \cite{AP}. It involves analyticity of certain
families of subspaces defined in terms of Schmidt vectors of the matrices
$\Phi(\z)$, $\z\in\T$. This characterization can be extended to the wider class
of {\em admissible} functions, i.e., the class of matrix functions $\Phi$ such
that the essential norm $\|H_\Phi\|_{\rm e}$ of the Hankel operator $H_\Phi$ is
less than the smallest nonzero superoptimal singular value of $\Phi$.
  In the final section we obtain a similar characterization of badly
approximable matrix functions.
