In this paper the characterization of those nonnegative linear lumping schemes is given which preserve the kinetic structure of the original system. The obtained result is a generalization of an earlier result by Hutchinson and Luss (1970, Chemical Engineering Journal, 1, 129-135). Applications to lower triangular reactions together with an algorithm to decide whether a reaction is lower triangular or not are also given. The examples from the fundamental paper by Li and Rabitz (1989, Chemical Engineering Science, 44, 1413-1430) are revisited.