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A laser beam machine is provided for irradiating a laser beam onto a workpiece to cut the same. When cutting a workpiece by irradiating a laser beam thereto, stable and reliable corner cutting is carried out according to a machining condition which provides practical effects. It is determined whether the machining (cutting) along a path according to a currently executed machining program has advanced to a corner B (Step S1), and if the corner B is reached, cutting is carried out according to a stepwise-varying machining condition M previously stored in a RAM (3) (Step S2). Specifically, the machining condition is once reduced to a low level or zero when the corner B is reached, and is thereafter increased stepwise up to a normal machining condition M.sub.0 with distance from the corner (with time). After the cutting of the corner B is completed, normal cutting is carried out according to the machining condition M.sub.0 (Step S3). Thus, it is possible to carry out stable and reliable cutting of the corner B according to the machining condition that provides practical effects.