A flat wire or a narrow strip has a profiled cross-section and is composed of a high-strength steel having the following composition (in weight-%): C 0.2-0.9%, Mn 12-25%, Si up to 0.5%, Al 0.5-2.0%, Cr 1.8-3.5%, S max. 0.005%, P max. 0.06%, N max. 0.1%, Mo max. 1.5%, B max. 0.01%, Ni max. 2.0%, Cu max. 2.0%, Ca max. 0.015%, Nb 0.02-0.35% and/or V 0.02-0.35%, and, as the remainder, iron and unavoidable, production-related contaminants. The wire or strip is cold-rolled and/or cold-profiled from wire-form precursor material, and has improved Rp0.2, Rm, and A80 mechanical values.