When solving a distributed problem based on a multi-agent system, the local behaviors of agents will be aggregated to the global behaviors of the multi-agent system towards a solution state. This paper presents a distributed discrete Lagrange multiplier (DDLM) method for solving distributed constraint satisfaction problems (distributed CSPs). In this method, the local behaviors of agents are aggregated as a descent direction of an objective function corresponding to the problem at hand. Thus, a trend to a solution state will be formed. Furthermore, we provide three techniques to speed up the aggregation of agents' local behaviors. Through experiments on benchmark graph coloring problems, we validate the effectiveness of the presented DDLM method as well as the three techniques in solving distributed CSPs.