Disclosed are a thin strip of an amorphous alloy having excellent workability, a nanocrystalline soft magnetic alloy which can stably provide good magnetic properties, and a magnetic core using the nanocrystalline soft magnetic alloy. The thin strip of an amorphous alloy is characterized in that the thin strip is formed of an alloy having a composition represented by Fe100-a-b-c-dMaSibBcCud (atomic %), wherein 0≦a≦10, 0≦b≦20, 4≦c≦20, 0.1≦d≦3, and 9≦a+b+c≦35, and containing unavoidable impurities, and, in the composition, M represents at least one element selected from Ti, V, Zr, Nb, Mo, Hf, Ta, and W, a Cu segregated part is present, on the surface side of the thin strip of the amorphous alloy, in which Cu is segregated at a higher concentration than the Cu concentration in the outermost surface part of the thin strip of the amorphous alloy, and the highest Cu concentration in the Cu segregated part is not more than 4 atomic %.