The invention discloses a soft magnetic amorphous alloy and a soft magnetic nanocomposite alloy formed from the amorphous alloy. Both alloys comprise a composition expressed by the following formula: (Fe1-x-yCoxMy)100-a-b-cTaBbNc where, M is at least one element selected from the group consisting of Ni and Mn; T is at least one element selected from the group consisting of Nb, W, Ta, Zr, Hf, Ti, Cr, Cu, Mo, V and combinations thereof, and the content of Cu when present is less than or equal to 2 atomic %; N is at least one element selected from the group consisting of Si, Ge, C, P and Al; and 0.01≦x+y≦0.5; 0≦y≦0.4; 1≦a≦5 atomic %; 10≦b≦30 atomic %; and 0≦c≦10 atomic %. A core, which may be used in transformers and wire coils, is made by charging a furnace with elements necessary to form the amorphous alloy, rapidly quenching the alloy, forming a core from the alloy; and heating the core in the presence of a magnetic field to form the nanocomposite alloy. The resulting nanocomposite alloy of the core comprises the amorphous alloy having embedded therein, fine grain nanocrystalline particles, about 90% of which are 20 nm in any dimension.