Magnetic tunneling junctions of La2/3Ca1/3MnO3/Eu2CuO4/ La2/3Ca1/3MnO3 have been fabricated by RF-magnetron sputtering, photolithography and ion beam etching. Tunneling effect was observed in these junctions by measuring their I-V curves. Interestingly, a discontinuity was observed in the I-V curves below the metal-insulator transition temperature (Tp) of La2/3Ca1/3MnO3 By changing temperatures, the discontinuity in I-V curves happens at the same voltage of 209mV, but starts at different currents. The discontinuity starting current (Ic) decreases with increasing temperature. There is a hysteresis near the discontinuity when the current increases and decreases. The discontinuity in I-V curves could indicate a novel switching process. This switching phenomenon occurs only in the ferromagnetic metal state and strongly suggesting a magnetic related effect. The physics of the switching process has not been understood yet, but it could be of interest for potential applications in spintronic devices.