Strands of a copper alloy containing 0.2 to 10 percent by weight of Sn are braided to form a stranded wire for a wire conductor for a harness having a conductor sectional area of 0.03 to 0.3 mm.sup.2. After the braiding, preferably stranded wire is heat treated so that its tensile strength is maintained at a prescribed level. The wire conductor for a harness has a breaking strength which is equivalent to that of a conventional harness wire, and is hardly broken by an impact. The wire conductor maintains its straightness, and strand ends do not fray upon cutting.