Abstract: A glassware molding machine includes a plunger and neck mold assembly that cooperates with a carriage and a parison blank mold to form a parison around a first vertical axis (46) in a forming station, and to suspend the completed parison by the neck ring portions. A pair of carriges, and body forming mold portions, alternately cooperate with the neck ring portions to form a container from the parison while the parison remains suspended by the neck ring portions and while the parison remains around the first vertical axis in the forming station. While one pair of forming mold portions transport a completed container from the forming station to a cooling and take-out station with the container held between the closed forming mold portions, the other pair of forming mold portions, are open and, with timing independent of the movement of the first pair move by rectilinear movement back to the forming station.