A method of connecting cables of a unitary pipe section that is to be assembled vertically to an undersea fluid transport pipe, by positioning around a low end of the unitary pipe section (40) a female annular connector (2) having connected thereto cables (14) extending along the unitary pipe section; positioning around a high end of the pipe (42) a male annular connector (24) having connected thereto cables (32) extending along the pipe; and connecting together the male and female connectors by sliding them vertically towards each other while assembling the unitary pipe section on the pipe.