The invention relates to a machine for blow-molding thermoplastic products. This type of machine has a molding unit comprising two mobile supports (12), which are hinged in relation to each other and which are controlled by a mechanism comprising a traveling slide (16), between an open position and a closed position. Each support (12) is connected to the slide (12) by at least one associated connecting link (36). The inventive blow-molding machine is characterized in that in its closed position, the main axes of the connecting links (36) are oriented in the same direction, perpendicular to the hinge axis (A1), in such a way that the control mechanism can cause the molding unit to be locked in this closed position.