Fault tree analysis is NP-hard problem. In this paper, we present a method which reduces size of the fault tree by eliminating the irrelevant events. Irrelevant event is the event which has no contribution to the system failure. In a fault tree, the irrelevant events occur due to the existence of the replicated events. By investigating the structure of the replicated events we establish the conditions which characterize the irrelevant events. Based on these conditions we present the computational algorithm which eliminate the irrelevant events. Complexity of the algorithm is shown to be polynomial and so, this algorithm can be utilized efficiently in FTA.