The present invention provides an amorphous alloy powder and magnetic powder cores exhibiting excellent high frequency properties and a method for making themof. The composition of said alloy powder by atomic percentage satisfies the following formula: (Fe1-xMx)100-a-b-cPaTbDc, wherein M represents at least one element of Co and Ni; T is over three elements selected from Al, C, B and Si, D is at least one element of Sn, Cr, Mn, Mo, W, V, Nb, Ta, Ti, Zr, Hf, Pt, Pd and Au; the subscripts x, a, b, and c satisfy the relationships 0.01≦x≦0.16, 8≦a≦15, 10≦b≦25 and 0.5≦c≦6. The said amorphous alloy powder is made by atomization method and a magnetic powder core comprises a molded article of mixture of the said alloy powder and an insulating material. A method of making the amorphous alloy powder core includes the steps of screening, insulating, compacting, annealing and spray painting.