We show that if f is a DC3 continuous map of a compact metric space then also f(N) is DC3, for every N > 0. This solves a problem given by [Li R. A note on the three versions of distributional chaos. Commun Nonlinear Sci Numer Simulat 2011:16:1993-1997]. (C) 2011 Elsevier B.V. All rights reserved.