Abstract: A method generates a machining program defining a trajectory of a tool for a workpiece having a first portion which can be machined with only linear axes followed by a second portion requiring a machining with linear axes and one or two rotational axes. A base code is generated defining the trajectory with, for the first portion, a first path by which relative movement occurs only along the linear axes followed by, for the second portion, a second path by which relative movement occurs along the linear axes and rotational axes. Before execution, the base code is optimized to modify the previously defined trajectory, including: modifying the first path with a relative movement occurring along the axes before starting on the second path; and reconstructing a profile of a kinematic quantity of one or both of the rotational axes on the first path to eliminate discontinuities on the profile.