The topic of 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 a binary relation modelling the attacks as in Dung’s 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). Since this kind of framework is relatively recent, the efficient computation of the main semantics remains an open question. In this paper, we propose one of the first algorithms dedicated to this issue. We prove the soundness and completeness of this algorithm.