By exploiting the special structure in the solution space of the maximum clique problem (MCP), an improved RLS method, the RLS-II method, is has been created where the neighborhood-moving direction of the local search is guided by the multivariate constraints constructed by the dying partitioning. Therefore, the probability of the local search approaching the optimal solution is increased. Using the absorbing Markov chain theory as a reference, the mathematical models of the RLS and RLS-II algorithms in solving maximum clique problem are constructed and the absorbing time of the two algorithms is analyzed. Moreover, the analytical results are experimentally demonstrated on 77 Benchmark instances. Both the theoretical analysis and simulation results show that the dying partitioning filter can effectively improve the performance of the RLS algorithm. Furthermore, the longer average length of the dying group, the higher probability and amplitude of the performance improvement.