This paper presents a method for reliability evaluation of a telecommunication network with variable link-capacities when the simple paths of the network are known. The LP-EM, suggested by Lee and Park (2001), identifies a composite path as a subnetwork and adds only a minimal set of links at each step which gives maximal increase on the maximum capacity flow of the subnetwork. Thereby the LP-EM reduces the possible occurrence of redundant composite paths significantly over other existing methods. Based on the LP-EM, our method further reduces the possible redundancy by identifying such simple paths that could give no increase of maximum capacity flow on the current subnetwork and excluding those simple paths from consideration in the process of constructing composite paths.