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(λ). In the case B = B*, the minimum number of matrix entries of W(λ) sufficient to uniquely determine Q is found.