Machine for cutting by electrical discharge machining by means of an electrode wire tensioned between and running between two guide heads each of which is mounted on an arm, one at least of the arms passing through an opening in one of the walls of a tight tank containing a machining liquid, this tank and this passing arm being able to move with respect to each other, this machine having a sealing plate masking this opening in the tank and having a hole in it to allow the arm to pass through it, linked by at least one seal to the passing arm and along which can slide the moving wall through which the arm passes, characterized by a deflecting device arranged so as to prevent transmission to the passing arm of any movement of the sealing plate in a direction perpendicular to the axis of this arm, thereby preventing asymmetric action on this arm of frictional and pressure forces due to the frictions that take place between the sealing plate and the moving wall of the tight tank and between the seal connecting the sealing plate and this passing arm.