The invention is related to a system (1) for converting fuel material comprising: a first reactor (2) in which a fuel material reacts with an oxide material for producing reaction products including fuel particles, ash and oxide particles, a second reactor (3) for oxidizing the oxide particles produced in the first reactor (2), a carbon separator (4) that receives fuel particles, ash and oxide particles produced in the first reactor (2) and suitable for separating the oxide particles and ash from the fuel particles, the carbon separator (4) comprising an outlet path (4c) for the oxide particles and ash exhaust, characterized in that said outlet path (4c) of the carbon separator (4) is connected to an ash separator (10) for separating the ash from the oxide particles.