  Downarowicz and Maass (2008) have defined the topological rank for all Cantor
minimal homeomorphisms. On the other hand, Gambaudo and Martens (2006) have
expressed all Cantor minimal continuous surjections as the inverse limits of
certain graph coverings. Using the aforementioned results, we previously
extended the notion of topological rank to all Cantor minimal continuous
surjections. In this paper, we show that taking natural extensions of Cantor
minimal continuous surjections does not increase their topological ranks.
Further, we apply the result to the minimal symbolic case.
