The soft magnetic properties of amorphous Fe-Si-B-Cu-Nb alloys are markedly improved by annealing the alloys above the crystallization temperature. The magnetic permeability of the annealed Fe74SixB22-xCu1Nb3 alloys shows a maximum value at an Si concentration of x=14. The precipitation of μ-Fe grains is observed for the annealing temperature giving the highest magnetic permeability. The lattice constant of the α-Fe phase shows a minimum at the annealing temperature yielding the highest magnetic permeability, and depends strongly on the Si concentration. The Si content in the μ-Fe phase estimated from the lattice constant is about 20 at% for Si concentrations above x=12. The volume fraction of the precipitated μ-Fe phase depends on the B concentration in the amorphous alloy. The grain size of μ-Fe at the optimum annealing temperature is about 130Å. To explain the mechanism of the high permeability, it is necessary to consider factors other than the grain size the volume fraction of the precipitated μ-Fe.