Stateless Model Checking (SMC) offers a powerful approach to verifying multithreaded programs but suffers from the state-space explosion problem caused by the huge thread interleaving space. The pioneering reduction technique Partial Order Reduction (POR) mitigates this problem by pruning equivalent interleavings from the state space. However, limited by the happens-before relation, POR still explores redundant executions. The recent advance, Maximal Causality Reduction (MCR), shows a promising performance improvement over the existing reduction techniques. However, MCR is limited to the dynamic information of the program and has to construct com- plicated constraints to ensure the feasibility of the derived execution. Unfortunately, the intricate constraints can greatly slow down the exploration of the state space. In this work, we present a new technique, which extends MCR with static analysis to reduce the size of the constraints, thus speeding up the efficiency of the state space exploration. We use system dependency graph to capture the dependency between a read and a later event e in the trace and identify those reads that e is not control dependent on. We then ignore the constraints over such reads and hence reduce the size of the constraints. The experimental results show that compared to MCR, the number of the constraints and the solving time by our approach are averagely reduced by 31.6% and 27.8%, respectively.