In the case of a laser processing machine (1) for processing workpieces (2) by means of a laser beam (3), comprising a work support (4) for workpieces (2) to be processed, a traversing unit (5), which can be made to traverse along one or a least two main axes (X, Y) in relation to the work support (4), and an optical processing unit (6), which is provided on the traversing unit (5) and focuses the laser beam (3) on the workpiece (2) to be processed, it is provided that the processing unit (6) is mounted pivotably at its one end (6a) with respect to the work support (4) on the traversing unit (5) about one or at least two additional axes (A, B), that a drive (7) is respectively provided for each additional axis (A, B) on the traversing unit (5) or on the processing unit (6) for deflecting the other end (6b) of the processing unit (6) with respect to the work support (4) about the respective additional axis (A, B), and that a controller (8) is provided, which divides a desired path of the laser beam (4) on the workpiece (2) into a movement of the traversing unit (5) along the one or at least two main axes (X, Y) and a deflection of the processing unit (6) about the one or at least two additional axes (A, B) and activates the drives (7, 8) of the traversing unit (5) and of the processing unit (6) correspondingly.