Community detection is very important in network data analysis. One of the most popular probabilistic models for fitting community structure is the stochastic block model (SBM). However, the SBM is not able to fully capture the dependence among edges from the same community. Various SBM approaches using the random effects are proposed to incorporate correlation among edges. However, this mainly designs for the exchangeable dependence structure, and also suffers high computational cost. In this talk, we propose a new community detection approach to utilize the dependence of network connectivity based on the estimating equation approach and the correlation matrix decomposition. The proposed method provides greater flexibility in handling different types of within-community dependence structure. In addition, the proposed algorithm does not involve specifying the likelihood function and direct estimation of correlation parameters, instead it utilizes two-step iteration procedure to detect true memberships of communities.