This work is related to a computational issue concerning an enriched abstract argumentation framework called RAF (‘Recursive Argumentation Framework’). A RAF is composed of a set of arguments and of a binary relation which models the attacks as in Dung’s seminal argumentation framework. The main difference between Dung’s framework and a RAF is the fact that a RAF is able to take into account higher-order interactions (i.e. an attack can target an attack and not only an argument). This kind of framework is recent enough for an efficient computation of its main semantics to remain an open question. In this paper, we propose one of the first algorithms dedicated to this issue, RAFDivider. We prove its soundness and its completeness.