Abstract This paper studies the fairness of achievable energy efficiency (EE) in a multicell multiuser multiple-input single-output downlink. The objective is to maximize the minimum EE among all base stations (BSs) subject to per-BS power constraints. The resulting optimization problem is a max-min fractional program, and, thus, difficult to solve in general. Our goal is to develop a decentralized algorithm for the max-min EE problem which solves the problem locally. The idea behind the proposed method is to combine the framework of successive convex approximation (SCA) and alternative direction method of multipliers (ADMM). We transform the convex program obtained at each step of the SCA procedure into a form that lends itself to the ADMM. The resulting formulation is solved optimally by allowing the BSs to exchange the required information until the ADMM converges. In addition to further reduce the backhaul overhead, the proposed algorithm is modified to enhance the convergence speed. Numerical results are provided to demonstrate the effectiveness of the proposed algorithms.