A pipe for a superconducting electrical connection, forming a unit intended to be connected at its ends for a formation of the superconducting electrical connection, includes a cryostat forming a pipe-in-pipe comprising an inner tube and an outer tube which are coaxial and a thermal insulator occupying the annular area between the outer tube and the inner tube; and a superconducting cable core housed inside the inner tube, the superconducting cable core having, at ambient temperature, an excess length with respect to the length of the cryostat such that, in its superconducting state, the length of the cable core is greater than or equal to the length of the cryostat.