Superconducting tapes having an inner laminate comprised of a parent-metal layer, a superconductive alloy layer on the parent-metal, a reactive-metal layer, and an outer laminate soldered thereon are joined in a superconducting joint by the method of this invention. The outer laminate, reactive-metal layer, and superconductive alloy layer are removed to form exposed sections of the parent metal layer. The tapes are positioned so that the exposed sections are in contact. Metallurgical bonding, for example by spot welding, forms bridges between the parent-metal layers. The joined exposed sections are heated in a protective atmosphere, and in the presence of excess reactive metal to form a continuous layer of the superconductive alloy on the bridge and the exposed areas that is continuous with the superconductive alloy layer on the superconducting tape. Optionally, sections of the outer laminate material corresponding to the size of the exposed sections are bonded to the outermost surfaces of the joined exposed sections.