A device for holding a turbine engine blade for purposes of machining, the device including a support including at least one housing in which at least one block is removably mounted, the block including two jaws presenting an opening for mounting an airfoil of a blade. The block further includes six presser points for pressing against the airfoil, and a movable presser finger for pressing against a pressure side surface or a suction side surface of the blade, the finger being moved by an actuation mechanism such that in a blade clamping position, the presser finger presses the blade against the presser points of the block, which itself is pressed against the support.