A printing machine for printing onto containers, such as bottles, having at least a conveyor and a printing unit with a print head module, with at least one print head, a movement system for adjusting the position of the print head module, a measuring system for determining the position of the print head module and a control unit for controlling the movement system, where the movement system comprises a radial module for adjusting the position of the print head module in the radial direction and a height module for adjusting the height of the print head module in the vertical direction.