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An Fe-based nano-crystalline alloy formed from an alloy composition of (FeE)(100-X-Y-Z)BXPYCuZ having an amorphous phase as a main phase, wherein 79≦100-X-Y-Z≦86 atomic %, 4≦X≦9 atomic %, 1≦Y≦10 atomic %, and 0.5≦Z≦1.2 atomic %, and wherein (FeE) includes Fe and at least one element selected from the group consisting of Ti, Zr, Hf, Nb, Ta, Mo, W, Cr, Al, Mn, Ag, Zn, Sn, As, Sb, Bi, Y, N, O and a rare-earth element, wherein a combined total of said at least one element selected from the group consisting of Ti, Zr, Hf, Nb, Ta, Mo, W, Cr, Al, Mn, Ag, Zn, Sn, As, Sb, Bi, Y, N, O and a rare-earth element is in an amount of 3 atomic % or less relative to the whole composition.