The aim of the invention is to produce electrically efficient equipotential connections in terms of resistivity between portions of a current return network of a non-conductive architecture, such as an airplane fuselage. The approach adopted according to the invention is to impart an equipotential bonding function to an aluminum cable having a large cross-section, said bond being electrically connected, via direct contact, to as many pieces of equipment as is physically possible.; According to one embodiment, an electrical connection assembly of an aircraft fuselage (100) having a composite skin comprises on-line shunt connections (2) for electrically interconnecting an aluminum alloy cable (1), having a large cross-section and serving as an equipotential bond, to brackets (113, 141) for primary current return networks and to brackets (111) for electrical devices via connections (202). Each on-line shunt connection (2) comprises a central sleeve (2m) for directly electrically contacting the cable (1), end portions for being assembled to the cable (1) by crimping, and an attachment means (2p) for attaching to the bracket (111) of the equipment. Each of the ends of the sleeve (2m) has seal accommodated therein. Each interconnection has two sealed areas, which surround a central contact area formed by means of window-stripping.