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We study the quantum discord dynamics of a bipartite composite system in the presence of a dissipative envi- ronment and investigate the effect of the interaction between the two subsystems.The results show that the interaction can influence the sudden transition between the quantum correlation and the classical correlation and for the maximally mixed marginals initial states, the sudden transition regime will always exist.The entangle- ments are also discussed in comparison to the quantum discord in describing the quantum correlations.