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This paper deals with the semigroup generation of anti-triangular operator matrices M with unbounded entries in Hilbert space. Based on the space decomposition, some necessary and sufficient conditions are given for M to generate contraction semigroups. In addition, the anti-triangular differential system, converted from the damping wave equation, is used to explain our work, and it is proved that the corresponding anti-triangular operator matrix satisfies the conditions and generates a contraction semigroup.