Unique Determination of a System by a Part of the Monodromy Matrix

First-order ODE systems on a finite interval with nonsingular diagonal matrix $B$ multiplying the derivative and integrable off-diagonal potential matrix $Q$ are considered. It is proved that the matrix $Q$ is uniquely determined by the monodromy matrix $W(\lambda)$. In the case $B = B^*$, the minimum number of matrix entries of $W(\lambda)$ sufficient to uniquely determine $Q$ is found.