A partitioning device between a machining station and a machine-tool driving station of the type driving at least two tool-holder rams is provided. The device includes a flexible curtain, called a central curtain, between two rams, where two ends are integral with a first ram and which is linked to the second ram. The relative movement of one ram with respect to the other along a first axis of movement, stretches more or less a length of curtain between the two rams.