Marek’s forward-chaining construction is one of the important techniques for investigating the non-monotonic reasoning. By introduction of consistency property over a logic program, they proposed a class of logic programs, FC-normal programs, each of which has at least one stable model. However, it is not clear how to choose one appropriate consistency property for deciding whether or not a logic program is FC-normal. In this paper, we firstly discover that, for any finite logic program ∏, there exists the least consistency property LCon(∏) over ∏, which just depends on ∏ itself, such that, ∏ is FC-normal if and only if ∏ is FC-normal with respect to (w.r.t.) LCon(∏). Actually, in order to determine the FC-normality of a logic program, it is sufficient to check the monotonic closed sets in LCon(∏) for all non-monotonic rules, that is LFC(∏). Secondly, we present an algorithm for computing LFC(∏). Finally, we reveal that the brave reasoning task and cautious reasoning task for FC-normal logic programs are of the same difficulty as that of normal logic programs.