A high-hardness constant-modulus alloy insensitive to magnetism which has a {110}<111> texture, a saturation magnetic flux density of 2,500-3,500 G, a temperature coefficient of Young's modulus at 0-40 C of (-5 to +5)10-5 C-1, and a Vickers hardness of 350-550; a balance spring comprising the alloy; a mechanical driving device; and a watch. An alloy comprising, in terms of atomic amount proportion, 20-40% cobalt, 7-22% nickel, 5-13% chromium, 1-6% molybdenum, and at least 37% iron as the remainder, provided that the sum of cobalt and nickel is 42.0-49.5% and the sum of chromium and molybdenum is 13.5-16%, is heated at a temperature not lower than 1,100 C and lower than the melting point thereof and then cooled. Thereafter, the alloy is repeatedly subjected to wiredrawing and an 800-950 C intermediate heat treatment.; The alloy is thereby wiredrawn to a reduction ratio of 90% or higher to obtain a wire of a fibrous structure having a fiber axis <111>. The wire is then subjected to cold working at a draft of 20% or higher to form a sheet. Subsequently, the sheet is heated at 580-700 C.