  We study the problem of finding a superoptimal solution to the four block
problem. Given a bounded block matrix function
$\left(\begin{array}{cc}\Phi_{11}
&\Phi_{12}\\\Phi_{21}&\Phi_{22}\end{array}\right)$ on the unit circle the four
block problem is to minimize the $L^\infty$ norm of $\left(\begin{array}{cc}
\Phi_{11}-F&\Phi_{12}\\\Phi_{21}&\Phi_{22}\end{array}\right)$ over $F\in
H^\infty$. Such a minimizing $F$ (an optimal solution) is almost never unique.
We consider the problem to find a superoptimal solution which minimizes not
only the supremum of the matrix norms but also the suprema of all further
singular values. We give a natural condition under which the superoptimal
solution is unique.
