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This paper presents a new Monte Carlo method to estimate the reliability of a large complex system represented by a reliability block diagram or by a fault tree. Two binary functions are introduced; one dominates the system structure function and the other is dominated by the structure function. These functions can be constructed easily by using part of path sets and cut sets of the system. Through the use of these binary functions, two variance-reducing techniques (control variate and importance sampling) are applied to the Monte Carlo evaluation of the system reliability. We prove that the new Monte Carlo method gives a reliability estimate with a smaller variance than that of the crude Monte Carlo method.