  Scalar-valued meromorphic Herglotz-Nevanlinna functions are characterized by
the interlacing property of their poles and zeros together with some growth
properties. We give a characterization of matrix-valued Herglotz-Nevanlinna
functions by means of a higher-order interlacing property. As an application we
deduce a matrix version of the classical Hermite-Biehler Theorem for entire
functions.
