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A laser beam machining method of processing a machining path having an acute angle in a CNC laser machining apparatus. A numerical control device (CNC) previously reads a machining program, to thereby detect an acute angle not greater than an allowable angle in the machining path. A machining operation is executed under normal machining conditions before a vertex (33) of the acute angle is reached and is stopped at the vertex (33) of the acute angle, and the region near the vertex (33) is cooled for a predetermined time by a cooling medium, whereby a lowering of the cut surface roughness due to an overheating by a laser beam (7) is prevented. After the cooling, the cutting work is executed under drilling conditions to continue the machining.