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It is shown that the $N$-dark soliton solutions of the integrable discretenonlinear Schr\"odinger (IDNLS) equation are given in terms of the Casoratideterminant. The conditions for reduction, complex conjugacy and regularity forthe Casorati determinant solution are also given explicitly. The relationshipbetween the IDNLS and the relativistic Toda lattice is discussed.Comment: First version was uploaded in 23 Jun 2005. Published in Journal of  the Physical Society of Japan in May, 200

Casorati Determinant Form of Dark Soliton Solutions of the Discrete Nonlinear Schrödinger Equation