Abstract: A method of fabricating at least one hollow glass article by implementing fabrication cycle consisting, specifically, in stretching the blank prior to inflating it by transferring the blank into a finishing mold that includes a suction cup in its mold cavity, the suction cup being movable in translation parallel to the axis of the mold over a stretching stroke between firstly an extended position inside the mold and secondly a retracted position in which the suction cup is situated at the bottom of the mold. The method includes the step of establishing suction in the suction cup prior to the bottom of the blank coming into contact therewith, thereby uniting the bottom of the blank with the suction cup while it is placed in its extended position, and then displacing the suction cup to its retracted position in order to stretch the blank.