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The traditional approach to handling functional dependence loops is based on Markov models, which are inefficient due to the well-known state space explosion problem. This paper proposes a new and efficient approach to handling functional dependence loops in the system reliability analysis. Based on the divide-and-conquer strategy, the approach transforms a system with functional dependence loops into subsystems without dependence or loops, which can then be solved using efficient combinatorial approaches. The proposed approach is applicable to analyzing complex systems with general component time-to-failure distributions. The basics and advantages of the proposed approach are illustrated through a detailed analysis of an example.