We have prepared Fe-Ni-system bilayer ribbons with different magnetostriction (compositions) and investigated the improvement of soft magnetic properties using the magnetoelastic effect. A toroidal core with D = 10 mm was made from the Fe6Ni94/Fe56Ni44 bilayer ribbon, and the B-H loop of the core was measured. The shape of the hysteresis loop dramatically changed depending on the inner layer (inner magnetic phase). This result indicates that the direction of the anisotropy induced by bending stress was changed depending on the inner layer. The slope of the B-H loop and coercivity reduced when the Fe56Ni44 layer was on the inner side. From the experimental results, we found that domain rotation was dominant for the magnetization process. Consequently, the increase in the coercivity over frequency could be suppressed by controlling the magnetization process. From these results, we found that a thin bilayer ribbon with positive and negative magnetostriction constant is an attractive material for reducing iron losses under high frequency.