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The interference alignment (IA) is a promising technique to efficiently mitigate interference and to enhance capacity of a wireless communication network. This paper proposes an interference alignment scheme for a network with multiple cells and multiple multiple-input and multiple-output (MIMO) users under a Gaussian interference broadcast channel (IFBC) scenario. We first extend a grouping method already known in the literature to a multiple-cells scenario and jointly design transmit and receiver beamforming vectors using a closed-form expression without iterative computation. Then we propose a new approach using the principle of multiple access channel (MAC) - broadcast channel (BC) duality to perform interference alignment while maximizing capacity of users in each cell. The algorithm in its dual form is solved using interior point methods. We show that the proposed approach outperforms the extension of the grouping method in terms of capacity and basestation complexity. Finally, a rate balancing technique is introduced to maintain fairness among users.