Building on the work of Ostrovsky (2008) on supply chain networks, Fleiner et al. (2016) showed that, in possibly cyclic trading networks under fully substitutable preferences, the set of fully trail-stable matchings is nonempty by characterizing it using the set of the fixed points of an increasing function. I characterize the fully trail-stable matchings using a different fixed point (increasing) function, rendering generalized T-algorithm for such environments. (C) 2017 Elsevier B.V. All rights reserved.