Abstract: 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; Q?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.