We propose a new method for computing transmit beamforming vectors for downlink multicell multiple-input multiple-output (MIMO) networks. The key novelty of the work is the application of graphical model theory to the intercell interference problem. An index restriction beamforming strategy is adopted to mitigate intercell interference, and is implemented with the well-known message-passing algorithm known as belief-propagation. The advantage of combining restricted index beamforming with belief propagation is only local channel information is required, and the computational complexity is lower than competing methods for base station cooperation. Numerical results show that the network throughput of downlink multicell MIMO systems is increased by the proposed cooperative method especially for cell edge users while the computational complexity is kept similar to non-cooperative methods.