A pedestal is fixed inside an outer casing of the flowmeter and a core is fixed on the pedestal. In one embodiment, the outer casing to which the core is fixed is rotated by a power roller, and slits are cut into the core by a laser beam apparatus. The cutting of such slits reduces the eddy current in such flowmeters. Depending on the movement of the laser apparatus with respect to the rotation of the outer casing, a spiral slit or a circular slit may be formed. Other patterns of slits may also be cut. A lathe may be used in place of the laser apparatus. The flowmeter includes an exciting coil, a measuring pipe and other necessary elements which are fixed to the outer casing after the slits are cut in the core.