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This paper proposes a decentralized model predictive control method based on a dual decomposition technique. A model predictive control problem for a system with multiple subsystems is formulated as a convex optimization problem. In particular, we deal with the case where the control outputs of the subsystems have coupling constraints represented by linear equalities. A dual decomposition technique is applied to this problem in order to derive the dual problem with decoupled equality constraints. A projected subgradient method is used to solve the dual problem, which leads to a decentralized algorithm. In the algorithm, a small-scale problem is solved at each subsystem, and information exchange is performed in each group consisting of some subsystems. Also, it is shown that the computational complexity in the decentralized algorithm is reduced if the dynamics of the subsystems are all the same. Numerical examples are given to show the effectiveness of the proposed method.