This paper considers the maximization of the weighted sum-rate (WSR) in multicell downlink multiple-input single-output (MISO) systems. The problem is non-convex and thus cannot be solved directly via conventional convex optimization methods. To achieve global optimality, we propose a novel monotonic optimization approach where a sensible search scheme first checks the feasibility of a chosen point and then utilizes a sequential partition method at each iteration to reduce the total number of feasibility evaluations. Besides, another relocating procedure also accelerates the convergence. Simulation results verify the improved convergence performance of the proposed approach compared with the previously proposed outer polyblock approximation algorithm and the branch-reduce-and-bound algorithm.