A device for sharpening a twist drill pointby means of a rotating grindstone (12) in a grinding machine comprises a base plate (14) lockably articulated around an axis parallel with the axis of the grindstone (12), a drill holder (16) for releasably holding a twist drill (1) to be sharpened, and a guide member (15). The guide member has a back plate (21) and a front plate (22), lockably rotatable in relation to each other. The back plate (21) is connected to the base plate (14) for movements in the direction of the grindstone axis, and the front plate (22) has guide means (28, 29) for slidably guiding the drill holder (16) in the general direction towards and away from the grindstone (12).