Abstract: A new global optimization reliability method, knowledge-based clustered partitioning method (KCP) for reliability problems involving correlated non-normal random variables, is proposed. Firstly, the isoprobabilistic transformation is adopted to transform the non-normal variables into the standard normal ones. Secondly, the Nataf transformation is used to transform the correlated non-normal random variables into the independent standard normal ones, which facilitate the sampling of the correlated non-normal random variables and reliability computation using the knowledge-based clustered partitioning method. To remove the limitations of the KCP with the binary step length and the KCP with equal step length, the KCP with changing step length is proposed, and the flowchart of reliability analysis using the KCP with changing step length is provided. Furthermore, a C-language based computer program is developed to carry out the reliability computations using the proposed KCP method. Finally, an example of reliability analysis for rock slope stability with plane failure is presented to demonstrate the validity and capability of the proposed method. The results indicate that the proposed knowledge-based clustered partitioning method can evaluate the reliability of rock slope stability involving correlated random variables accurately and efficiently. Furthermore, the global optimization solutions can be determined using the proposed KCP method. The proposed KCP method can result in the same accuracy as the traditional Monte Carlo simulations, and its efficiency is significantly higher than that of the traditional Monte Carlo simulations. More importantly, the KCP with changing step length can ensure an optimal balance between the accuracy and the efficiency of reliability computations.