Curtain air bag unit for a motor vehicle is provided which comprises an air bag extending parallel to the longitudinal axis of the motor vehicle. Further it comprises fixing means for fixing the air bag in the area of the roof bar of the motor vehicle, whereby the fixing means comprise a tension member, that extends from a first fixing element to a second fixing element. It also comprises tensioning means for influencing the tensile stress of the tension member during mounting of the curtain air bag unit into the motor vehicle. A pre-cut tension member can be used whose length is chosen in a way that the mounting in the vehicle can be carried out simply and conveniently.