Coordinated multi-point transmission/reception (CoMP), in which base stations (BSs) cooperate during the downlink, has been identified as a tool for improving user rates and mitigating interference. The cost for existing coordination schemes with joint processing is the heavy exchange of channel state information and signal information over backhaul links. In this paper, we propose a decentralized BS processing method for the downlink of CoMP systems. Its key feature is that each BS performs decentralized processing without requiring any explicit information exchange between BSs. Unlike existing work, each BS maximizes the rate for multiple intra-cell users and cancels inter-cell interference in a decentralized manner.