Method for tearing off and rolling up a strip of absorbent fiber sheet for a tampon, comprising the steps of - providing an endless absorbent fiber sheet along a machine direction; - providing weakened division lines to said endless absorbent fiber sheet essentially along a cross direction perpendicular to said machine direction; - frictionally pulling on the absorbent fiber sheet with a first linear speed at a first position along the machine direction; - frictionally pulling on the absorbent fiber sheet with essentially at least the first linear speed at a second position along the machine direction, said second position being downstream of the first position with respect to the machine direction; - optionally guiding the absorbent fiber sheet by one or more movable guiding means towards a third position, said third position being downstream of the first and second position with respect to the machine direction. - tearing off a strip of absorbent fiber sheet from the endless absorbent fiber sheet by pulling on the absorbent fiber sheet at a third position along the machine direction, said third position being downstream of the first and second position with respect to the machine direction, said pulling inducing a second linear speed on the absorbent fiber sheet at the third position which is larger than said first linear speed, thereby inducing an effective tearing force on the sheet between the first and the third position, - rolling up the strip of absorbent fiber sheet, characterized in that at the first position the absorbent fiber sheet is essentially maintained at the first linear speed and that at the second position the absorbent fiber sheet is allowed to obtain a speed at said second position which is higher than the first linear speed when the sheet is being pulled at the third position. - providing an endless absorbent fiber sheet along a machine direction; - providing weakened division lines to said endless absorbent fiber sheet essentially along a cross direction perpendicular to said machine direction; - frictionally pulling on the absorbent fiber sheet with a first linear speed at a first position along the machine direction; - frictionally pulling on the absorbent fiber sheet with essentially at least the first linear speed at a second position along the machine direction, said second position being downstream of the first position with respect to the machine direction; - optionally guiding the absorbent fiber sheet by one or more movable guiding means towards a third position, said third position being downstream of the first and second position with respect to the machine direction. - tearing off a strip of absorbent fiber sheet from the endless absorbent fiber sheet by pulling on the absorbent fiber sheet at a third position along the machine direction, said third position being downstream of the first and second position with respect to the machine direction, said pulling inducing a second linear speed on the absorbent fiber sheet at the third position which is larger than said first linear speed, thereby inducing an effective tearing force on the sheet between the first and the third position, - rolling up the strip of absorbent fiber sheet,