The invention relates to a method for machining a transparent workpiece (4) by generating non-linear absorption of laser radiation in a laser beam focus located in a volume of the workpiece (4). The object of the invention is that of providing a method of improved precision and quality, and a corresponding device, for laser machining of workpieces. In particular, it is also intended for it to be possible for workpieces made of composite materials or of other special materials, such as filter glass, to be machined at an improved level of quality. For this purpose, the method according to the invention comprises the following steps: spectroscopic measurement of the linear absorption of the laser radiation in the workpiece (4), selecting a working wavelength at which the linear absorption is low, and machining the workpiece (4) by means of application of laser radiation at the working wavelength. The invention furthermore relates to a corresponding device for machining a transparent workpiece (4).