The invention relates to an arrangement in a mechanical shaft seal. The arrangement comprises at least one sealing part rotating with a shaft in relation to a frame of the device and at least one sealing part fastened to the frame and/or to a separate frame part that is non-rotatable in relation thereto. The arrangement also comprises at least one additional part arranged to connect the frame and the sealing part that is non-rotatable in relation thereto and to prevent the rotation of the sealing part in relation to the frame. At least one set of the additional parts is memory metal elements.