Summary: This paper presents a modified algorithm to node elimination process for computing the upper-bound reliability of two-terminal networks. The algorithm has two technique; nodes removal and decomposition technique. The first technique is a modified algorithm to node elimination process. Such that the node elimination process can be eliminate the nodes one by one, but the first technique eliminates the all nodes in one step to abbreviate the time of calculation the upper-bound reliability of the network. The second technique decomposes a large network into two sub-networks at appropriate cut-nodes to simplify the computation of the upper-bound reliability of the network types. It uses the first technique to remove the nodes and compute the upper-bound reliability of that networks. The algorithm is conceptually clearer and requires less work for its implementation. The results of using the algorithm for an example could simplify the calculation of the reliability more than another method.