For a multiuser multi-input multi-output (MU-MIMO) multicell network, the Han-Kobayashi strategy aims to improve the achievable rate region by splitting the data information intended to a serviced user (UE) into a common message and a private message. The common message is decodable by this UE and another UE from an adjacent cell so that the corresponding intercell interference is cancelled off. This work aims to design optimal precoders for both common and private messages to maximize the network sum-rate, which is a highly nonlinear and nonsmooth function in the precoder matrix variables. Existing approaches are unable to address this difficult problem. In this paper, we develop a successive convex quadratic programming algorithm that generates a sequence of improved points. We prove that the proposed algorithm converges to at least a local optimum of the considered problem. Numerical results confirm the advantages of our proposed algorithm over conventional coordinated precoding approaches where the intercell interference is treated as noise.