The screen-printing machine (10) comprises: a print station (12); at least one support surface (40A, 40B) for supporting the objects away from the print station (12); and at least one transfer device (18, 20) for transferring an object, which transfer device comprises a manipulator arm (54) equipped with an end clamp (56), the arm (54) being hinged relative to the support surface (40A, 40B) about a pivot axis (Z1-Z1) and the clamp (56) being hinged relative to the arm (54) about a tilt axis. The pivot axis (Z1-Z1) of the arm (54) defines with the normal to the support surface (40A, 40B) a non-zero angle of inclination that is less than 45.degree.. Application to printing flasks.