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To increase the saturation magnetization (M_s) of commercially available soft magnetic Finemet alloys to the level comparable to that of Si-steel and Fe-based nanocrystalline alloys such as Nanoperm, Nanomet, the B or Si content in combination with annealing heat treatment was tailored. The ribbons of Fe_{95−<i>x</i>}Si₁B<i>_x</i>Nb₃Cu₁ (<i>x</i> = 11, 12, 13) and Fe_{87−<i>x</i>}Si<i>_x</i>B₉Nb₃Cu₁ (<i>x</i> = 6, 8, 10) were prepared by melt-spinning and annealed at different temperatures to develop nanocrystalline microstructure optimizing the soft magnetic properties. The magnetic properties of the as-spun and annealed ribbons were measured using a vibrating sample magnetometer and AC B-H loop tracer to acquire M_s of above 1.4 T in all as-spun ribbons. Among the alloys, Fe₈₄Si₁B₁₁Nb₃Cu₁ annealed at 545 °C showed the highest M_s of 2 T, which exceeds that of the conventional Finemet and other Fe-based nanocrystalline alloys.