Two-mode stochastic local search (SLS) and focused random walk (FRW) are the two most influential paradigms of SLS algorithms for the propositional satisfiability (SAT) problem. Recently, an interesting idea called configuration checking (CC) was proposed to handle the cycling problem in SLS. The CC idea has been successfully used to improve SLS algorithms for SAT, resulting in state-of-the-art solvers. Previous CC strategies for SAT are based on neighboring variables, and prove successful in two-mode SLS algorithms. However, this kind of neighboring variables based CC strategy is not suitable for improving FRW algorithms. In this paper, we propose a new CC strategy which is based on clause states. We apply this clause states based CC (CSCC) strategy to both two-mode SLS and FRW paradigms. Our experiments show that the CSCC strategy is effective on both paradigms. Furthermore, our developed FRW algorithms based on CSCC achieve state-of-the-art performance on a broad range of random SAT benchmarks.