The main purpose of this article is to explore the relationship of two existing conditions for the triangular decoupling problem. The first one is the triangular-diagonal-dominance condition proposed by Hung and Anderson. The second one is the stable coprime factorisation-described condition proposed by Gomez and Goodwin, which has been proven as a necessary and sufficient condition for the triangular decoupling problem. This article proves that the two conditions are actually equivalent. It also provides easy-to-use criteria for assessment of the solvability of the triangular decoupling problem.