The proposition about optimum factorization of a non-negative matrix function $f(\lambda )$ is generalized for the case where the unknown function $A(z)$ of class $H_2 $ satisfies the inequality \[ A\left( {e^{ - i\lambda } } \right)A^ * \left( {e^{ - i\lambda } } \right) \leqq 2\pi f(\lambda ) \] instead of the usual equality \[ A\left( {e^{ - i\lambda } } \right)A^ * \left( {e^{ - i\lambda } } \right) = 2\pi f(\lambda ). \].