The matrix-valued Weyl-Titchmarsh functions M (λ) of vector-valued Sturm-Liouville operators on the unit interval with the Dirichlet boundary conditions are considered. The collection of the eigenvalues (i.e., poles of M (λ)) and the residues of M (λ) is called the spectral data of the operator. The complete characterization of spectral data (or, equivalently, N × N Weyl-Titchmarsh functions) corresponding to N × N self-adjoint square-integrable matrix-valued potentials is given, if all N eigenvalues of the averaged potential are distinct.