Movable ballast screening system capable of moving parallel to a working direction, comprising - a screening apparatus comprising at least one first screen having a first fouled ballast inlet, a first cleaned ballast outlet located in front of the first fouled ballast inlet in a first direction parallel to the working direction and a first discarded ballast outlet, and at least one second screen having a second fouled ballast inlet located behind the first fouled ballast inlet in the first direction, a second cleaned ballast outlet located behind the first cleaned ballast outlet and in front of the second fouled ballast inlet in the first direction and a second discarded ballast outlet, - a set of one or more rerouting conveyors suitable for collecting and conveying, in the first direction, an output flow from the second cleaned ballast outlet and an output flow from the first cleaned ballast outlet, the set of one or more rerouting conveyors comprising one or more rerouting collection conveyors for directly collecting the output flow from the second cleaned ballast outlet and for conveying it in the first direction, - a set of one or more discard conveyors suitable for collecting and conveying, in a second direction parallel to the working direction and opposite the first direction, a flow of discarded ballast coming from the first discarded ballast outlet and a flow of discarded ballast coming from the second discarded ballast outlet, the set of one or more discard conveyors comprising one or more first discard collection conveyors (32.1), located directly beneath the first discarded ballast outlet for collecting a flow of discarded ballast coming from the first screen and for conveying it in the second direction, characterized in that - the one or more rerouting collection conveyors extend beneath the first screen at a height lower than the one or more first discard collection conveyors, and - the second screen comprises a discarded ballast inlet suitable for being fed by the one or more first discard collection conveyors, and a chute for sending the flow of discarded ballast coming from the first screen from the discarded ballast inlet to the second discarded ballast outlet. - a screening apparatus comprising at least one first screen having a first fouled ballast inlet, a first cleaned ballast outlet located in front of the first fouled ballast inlet in a first direction parallel to the working direction and a first discarded ballast outlet, and at least one second screen having a second fouled ballast inlet located behind the first fouled ballast inlet in the first direction, a second cleaned ballast outlet located behind the first cleaned ballast outlet and in front of the second fouled ballast inlet in the first direction and a second discarded ballast outlet, - a set of one or more rerouting conveyors suitable for collecting and conveying, in the first direction, an output flow from the second cleaned ballast outlet and an output flow from the first cleaned ballast outlet, the set of one or more rerouting conveyors comprising one or more rerouting collection conveyors for directly collecting the output flow from the second cleaned ballast outlet and for conveying it in the first direction, - a set of one or more discard conveyors suitable for collecting and conveying, in a second direction parallel to the working direction and opposite the first direction, a flow of discarded ballast coming from the first discarded ballast outlet and a flow of discarded ballast coming from the second discarded ballast outlet, the set of one or more discard conveyors comprising one or more first discard collection conveyors (32.1), located directly beneath the first discarded ballast outlet for collecting a flow of discarded ballast coming from the first screen and for conveying it in the second direction, - the one or more rerouting collection conveyors extend beneath the first screen at a height lower than the one or more first discard collection conveyors, and - the second screen comprises a discarded ballast inlet suitable for being fed by the one or more first discard collection conveyors, and a chute for sending the flow of discarded ballast coming from the first screen from the discarded ballast inlet to the second discarded ballast outlet.