Using a Cu stabilized strand with Nb matrix, a 30 meter long Rutherford cable was made by a collaboration of Fermilab and NIMS. Recently the strand and cable were tested. In both cases instability was observed at around 1.5 Tesla. The magnetization of this strand was measured first using a balanced coil magnetometer at 4.2 K. Strands showed an anomalously large magnetization behavior around at 1.6 T, which is much higher than the usual (4.2 K) of Nb matrix. This result is compared with the magnetization data of short strand samples using a SQUID magnetometer, in which a flux-jump signal was observed at 0.5 Tesla, but not at higher field. To explain this magnetization anomaly, the interfilament coupling through the thin Nb films in the strands due to the proximity effect, which is preventing the full penetration of the external field into the inside part of strand, is suggested. The instability problems observed in low field regions of the Rutherford cables and the small racetrack magnet wound with this cable are attributed to this effect.