PURPOSE: To make it possible to cut and remove properly an indeterminate part by detecting existence of the indeterminate part by means of radioactive rays emitted from a steel plate and by determining a cutting plane line according to the shape of the indeterminate part, in an apparatus with which the indeterminate part of a tip part and a tail part of the steel plate are cut and removed.

CONSTITUTION: A detector 24 is breadth wise provided on a steel plate 2 being a travelling body, and existence of an indeterminate part and subsequent two levels of the steel plate 2 are detected using infrared rays emitted from the steel plate 2. And, when the presence of a fishtail at the tip part of the steel plate 2 is found, a cutting line shall be determined at the position where the width right beneath the detector 24 of the steel plate 2 equals to the set width after a root part B of the fishtail passes through just under the detector 24. On the other hand, one light level is detected by the detector 24, and in case the tip part of the steel plate 2 is found to have a tongue shape, the cutting line 26 is determined at the position where the width just under the detector 24 of the steel plate 2 becomes equal to the set value, thereby allowing the indeterminate part being cut are removed precisely from the steel plate 2.