rotated by a drill string results from the fact that the torque about the bit decreases as a function of an increase in the rotary speed the present invention proposes that the appearance of the stick slip dysfunction be prevented by making the behaviour of the drill bit stable at the rotary speed by acting upon the cause of the instability to that effect two methods are preferably used and illustrated by fig5 and 6 in fig5 curve 17 represents the resistant torque about the drill bit within the range of rotary speeds n1 and n2 curve 18 represents a friction torque provided by suited means secured with the drill bit or the drill collars during operation between rotary speeds n1 and n2 the overall torque about the drill bit is the sum of the torque about the bit and of the additional torque the overall torque is represented here by curve 19 resulting from the addition of curve 17 and curve 18 the friction means are determined to generate a friction curve 18 which increases with the rotary speed the overall rotation resistance at the level of the drill bit is thus represented by a curve 19 which increases as a function of speed under these conditions when the rotary speed of the string varies within the range.