A multiple-layer braided line having a high tensile strength composite steel core in which the innermost braided fibrous sheath layer is nylon, securely bonded to the composite steel core. An outer braided fibrous sheath is polyester formed over the inner sheath. The core is selected with a tensile strength over the desired rate load-carrying ability of the line, but less than that of the overall tensile strength of the inner and outer sheaths. The line is lightweight and has a high tensile strength and improved resistance to severing, melting and burning results, suitable for use by mountaineers, firemen and rescue workers. The line substantially eliminates backlash.