We propose an improvement of our previous work (Cayrol, C., Lagasquie-Schiex, M.C.: Logical encoding of argumentation frameworks with higher-order attacks and evidential supports. International Journal on Artificial Intelligence Tools 29(3-4), 2060003:1–2060003:50 (June 2020). https://doi.org/10.1142/s0218213020600039). This work concerned a logical encoding of argumentation frameworks with higher-order interactions (i.e. attacks/supports whose targets are arguments or other attacks/supports) with an evidential meaning for supports (such frameworks are called REBAF). Then this encoding has been used for giving a characterization of REBAF semantics. We show in the current paper that the encoding proposed in [25] has some weaknesses when support cycles exist in the REBAF. Our aim is to solve these weaknesses and so to propose a new characterisation that allows to take into account support cycles whatever is the type of these support cycles.