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This paper investigates max-min beamforming for the multicell downlink transmission, where multiple base stations (BSs) cooperatively optimize their transmit beamforming vectors using long-term channel statistics. Based on Lagrangian duality, we reformulate the original problem into a dual uplink problem, which is expected to achieve the same optimal signal to interference plus noise ratio (SINR) as the primal downlink problem. The normalized dual uplink beamformer is the dominant eigenvector of a generalized eigenvalue decomposition (GEVD) problem, and the dual uplink transmit power can be solved iteratively. According to the duality theory, we develop an iterative algorithm and compare it with the beamformer-power iterative algorithm extended from. Simulation results verify the computational efficiency of the proposed algorithm.