The degradation mechanism of soft magnetic properties of $Fe-Hf-N/Cr/SiO_2$ thin films reacted with a bonding glass was investigated. When $Fe-Hf-N/Cr/SiO_2$ films were annealed under $600^{circ}C$ without the bonding glass, the compositions and the soft magnetic properties of Fe-Hf-N layers were not changed. However, after reaction with the bonding glass at $550^{circ}C$, the soft magnetic properties of the film were degraded. At $600^{circ}C$, the saturation magnetization of the reacted film decreased to 13.5 kG, and its coercivity increased to 4 Oe, and its effective permeability decreased to 700. It was founded that O diffused from the glass into the Fe-Hf-N layers during the reaction and generated $HfO_2$ phases. It was considered that the soft magnetic properties of the $Fe-Hf-N/Cr/SiO_2$ films reacted with the bonding glass were primarily degraded by the formation of the Fe-Hf-O-N layer of which the Fe content was below 60 $at\%$, and secondarily degraded by the Fe-Hf-O-N layer above 70 $at\%$.