This paper considers the consensus problem of Lipschitz type nonlinear multi-agent systems with quite general communication topologies. Based on relative states information of neighbor agents, static consensus controllers are proposed. Special matrix decomposition is performed on the graph Laplacian matrix which can be factored into the product of two specific matrices. Base on this property of graph Laplacian matrix, a novel analysis method for consensus is introduced in which the consensus problem is converted into a stabilization problem of a system with lower dimensions by performing a proper variable transformation. Sufficient conditions are obtained based on Lyapunov stability analyses. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.