Electrodeposited CoNiFe soft magnetic films with high B_s were investigated for use as head core materials. It was found that a film consisting of an fcc phase structure with low Fe content has low magnetostriction of +2∼+6 × 10^-6. When the film composition was fixed at Co₆₂Ni₁₂Fe₂₆, the operating conditions for obtaining soft magnetic properties were optimized It was found that soft magnetic thin films composed of fine crystals 10-15 nm in diameter were obtained in conditions of low pH (< 3.0) and low current density (< 40 mAcm^-2). In these operating conditions, a current efficiency of less than 80% with hydrogen evolution during the CoNiFe deposition was confirmed to be one of key factors for obtaining soft magnetic CoNiFe films with a suitably high B_s value. A typical Co₆₂Ni₁₂Fe₂₆ film had the following properties. B_s=2.0 T, H_c=1.7 Oe, and λ_s=+4.9×10^-6.