The invention concerns a single-unit element of underwater pipe for a seafloor-surface connection, consisting of an assembly of two coaxial PiP-type pipes (1) comprising an inner pipe element (2) and an outer pipe element (3) with an annular space (4i) therebetween, preferably including a thermal insulation material (42) in said annular space and including at each end a steel-forged junction piece (6, 6a-6b) for connecting said two single-unit elements of coaxial pipes (1), said junction pieces (6) being welded both at the ends of said inner pipes and at the ends of said outer pipes. The invention is characterized in that said inner pipe element (2) comprises in its main part an inner metal tube (20) with reduced thickness relative to the thickness of the ends of said inner pipe welded to said junction pieces (6), the inner tube (2) being coated with a material (22) comprising longitudinal continuous fibers wound about said inner tube so as to completely cover the surface of said inner tube.