A method for installing a self-supporting tower at a sea bed. An anchoring mechanism (32) is installed on the bed. A float (18) and a tubular pipe (68) are submerged and then driven towards the bed (12) to attach to one of the ends (72) of the anchoring mechanism (32), while the float (18) is fastened to the other (70) of the ends keeping the pipe (68) vertical above the anchoring mechanism (32). The tubular pipe (68) and the float (18) are supplied separately. The float (18) is kept submerged at a distance away from the anchoring mechanism (32). The tubular pipe (68) is suspended from the float via the other (70) of the ends of the pipe.