in the drafting device 18 with a nipping point of the front rollers 17 as a fixed point thereby forming balloon turning also in the direction of arrow b in the belt type false twister 21 as shown in detail in fig1 and 3 two endless belts 24 and 25 crossing each other in a generally x shape are respectively stretched between and entrained about driving pulleys 26 27 and driven pulleys 28 29 the pulleys 26 27 28 and 29 are supported rotatably through bearings on arm like frames 32 and 33 projecting fixedly from a machine frame 31 the endless belts 24 and 25 are driven in the arrowed direction in the figure to false twist the fiber bundle in the direction of arrow c the spacing between the driving pulleys 26 27 and the driven pulleys 28 29 is urged in an expanding direction by means of a known tension device it is required to permit the disposing of a later described pressing roller device 34 between the driving pulley 26 and the driven pulley 28 preferably the said spacing is large the position and direction of the pulleys 26 27 and 28 29 are set so that when the belts 24 and 25 are entrained naturally about the pulleys 26 27 and 28 29 there remains a slight gap therebetween and the following pressing roller device 34 is disposed between one pulleys 26 and 28 a lever 36 is mounted on one arm like frame 32 pivotably through a pin 35 and a roller 37 is mounted rotatably on a free end of the lever 36 when the lever 36 is urged in the arrowed direction in fig1 by means of an air cylinder 38 the roller 37 comes into rolling contact with.