Abstract: In order to sever heads of fish or, in the case of pre-decapitated fish collar bones remaining on the torso from the torso at a preset location (38) with a blade (11) whose cutting edge runs transversely to the orientation of the fish, the fish must be aligned relative to the blade's cutting plane (39). Since in known methods and apparatus and particularly regarding differing fish size difficulties occur in precisely engaging the fish for the purpose of displacing them as well as due to their deformation in obtaining the correct positioning, it is proposed that the fish be gripped in form-locking relationship at a dimensionally stable location such as the head by a movable positioning device (4) and displaced in a direction towards the cutting plane (39) until the preset location (38) lies in the cutting plane.