Method for controlling a moulding unit for forming a thermoplastic container by blow-moulding, notably by stretch-blow-moulding, of a preform, the moulding unit comprising: - a carriage which carries fixedly a mould bottom and which is mounted with the ability to move in a fixed support between a lower position for extracting the finished container and an upper position for moulding a base of the container; - first actuating means for moving the carriage relative to its fixed support between the lower extraction position and an intermediate initial boxing position in which the bottom can be enclosed between two half-moulds in a closed-together position; - second actuating means for moving the carriage relative to its fixed support from the intermediate initial boxing position to the upper moulding position, the second actuating means comprising at least one cylinder, fixed with respect to the support and housing a piston that divides the cylinder into a lower working chamber and an upper chamber, the piston being able to slide between a lower resting position and a upper boxing position in which it pushes the carriage to its upper moulding position by pressurizing a working fluid in the lower working chamber, relative to the pressure in the upper chamber; - third actuating means for moving the carriage from its upper moulding position to its lower extraction position; the method comprising a step of extracting a finished container, which takes place after the carriage has been pushed to its upper moulding position by the piston, during which the carriage is moved from its upper moulding position to its lower extraction position by the third actuating means; characterized in that, during the extraction step, the moving of the carriage by the third actuating means is initiated while the piston has not yet returned to its lower resting position, the carriage pushing the piston to its lower resting position, at least over a final portion of its travel to its lower extraction position. - a carriage which carries fixedly a mould bottom and which is mounted with the ability to move in a fixed support between a lower position for extracting the finished container and an upper position for moulding a base of the container; - first actuating means for moving the carriage relative to its fixed support between the lower extraction position and an intermediate initial boxing position in which the bottom can be enclosed between two half-moulds in a closed-together position; - second actuating means for moving the carriage relative to its fixed support from the intermediate initial boxing position to the upper moulding position, the second actuating means comprising at least one cylinder, fixed with respect to the support and housing a piston that divides the cylinder into a lower working chamber and an upper chamber, the piston being able to slide between a lower resting position and a upper boxing position in which it pushes the carriage to its upper moulding position by pressurizing a working fluid in the lower working chamber, relative to the pressure in the upper chamber; - third actuating means for moving the carriage from its upper moulding position to its lower extraction position;