A work method for a Cartesian machine tool, the method comprising the following steps: - starting machining of a workpiece; - carrying out a machining cycle; - carrying out a qualification operation, i.e., an operation to check a relative positioning system, on board the machine tool, by way of comparison with a positioning system with absolute reference for calibration, which is adapted to check the displacement of the indications of the positioning system on board the machine, i.e., of the relative reference system, with respect to the positions of the absolute reference system for calibration; - checking the outcome of the qualification operation; - if the qualification operation is passed successfully, that is if the displacement of the indications of the positioning system on board the machine with respect to the positions of the absolute reference system fall within a preset range of tolerances, then proceed with an operation to measure the workpiece prior to finishing; - if the qualification is not passed, that is if the displacement of the indications of the positioning system on board the machine with respect to the positions of the absolute reference system do not fall within a preset range of tolerances, then proceed with a compensation step, which comprises one or more compensation operations; - carrying out a finishing cycle; - measuring the finished workpiece; - ending machining; characterized in that said compensation operations comprise electronic compensations and active compensations, said electronic compensations being electronic operations adapted to correct a feedback loop of the machine and including setting up a table of independent displacements that makes each axis of the machine describe the correct path using the displacements of the concurrent axes of the machine tool on the basis of the qualification cycle carried out with the absolute reference system for calibration, said active compensations consisting of mechanical and electro-hydraulic operations that modify the geometry of the machine and are adapted to recover the displacements measured during the qualification operations. - starting machining of a workpiece; - carrying out a machining cycle; - carrying out a qualification operation, i.e., an operation to check a relative positioning system, on board the machine tool, by way of comparison with a positioning system with absolute reference for calibration, which is adapted to check the displacement of the indications of the positioning system on board the machine, i.e., of the relative reference system, with respect to the positions of the absolute reference system for calibration; - checking the outcome of the qualification operation; - if the qualification operation is passed successfully, that is if the displacement of the indications of the positioning system on board the machine with respect to the positions of the absolute reference system fall within a preset range of tolerances, then proceed with an operation to measure the workpiece prior to finishing; - if the qualification is not passed, that is if the displacement of the indications of the positioning system on board the machine with respect to the positions of the absolute reference system do not fall within a preset range of tolerances, then proceed with a compensation step, which comprises one or more compensation operations; - carrying out a finishing cycle; - measuring the finished workpiece; - ending machining;