A steel wire is composed mainly of fine pearlite and/or coarse pearlite, where the lamellar cementite in the pearlite is amorphous or amorphous-like. Alternatively, the wire may be composed mainly of bainite, where the cementite in the bainite is amorphous or amorphous-like. To manufacture the steel wire, a starting steel product is subjected repeatedly to patenting and cold drawing, and then subjected to final drawing at a true strain of 2.0 or above while cooling. The steel wire is higher in strength and toughness than wire whose lamellar cementite consists of nano crystals. The steel wire does not suffer any delamination when subjected to torsion.