A method of laying an off-shore pipe comprising: - installing in a target position on the seabed a fixed receiving structure having a redirecting device for a damping cable, - on a laying vessel, providing the pipe with an initial end length to which a pipeline end termination device is mounted, - connecting an underwater suspension buoy to the pipeline end termination device, the underwater suspension buoy applying to the pipeline end termination device a suspension force which is directed vertically upwards, - paying-out a first length of the pipe with the pipeline end termination device from the laying vessel vertically towards the seabed to a provisional anchoring position, in which the initial end length has an approximately vertical orientation with a vertical safety distance between the pipeline end termination device and the seabed, - extending a damping cable from the pipeline end termination device through the redirecting device to an underwater damping buoy, so that the damping cable, slidingly supported and redirected by the redirecting device and tensioned by a buoyancy force of the damping buoy, forms a damping provisional anchoring of the pipeline end termination device to the fixed receiving structure, characterised by: - moving the laying vessel horizontally away from the fixed receiving structure and paying-out, from the laying vessel, a further length of the pipe so as to incline the initial end length progressively from the vertical orientation towards a horizontal orientation up to a lowered position, - with the initial end length in the lowered position, moving the laying vessel to positioning the initial end length in horizontal direction in a final abutment position with respect to said target position, then abutting the pipeline end termination device in the final abutment position, - during the steps of inclining to the lowered position and of horizontally positioning the initial end length: - using the suspension force of the suspension buoy to counterbalance at least part of the weight of the pipeline end termination device, - using the buoyancy force of the damping buoy to counterbalance a pulling force of the initial end length of the pipe and to damp the movements of the initial end length of the pipe, - using the sliding support of the redirected damping cable to allow relative compensation movements between the pipeline end termination device and the fixed receiving structure. - installing in a target position on the seabed a fixed receiving structure having a redirecting device for a damping cable, - on a laying vessel, providing the pipe with an initial end length to which a pipeline end termination device is mounted, - connecting an underwater suspension buoy to the pipeline end termination device, the underwater suspension buoy applying to the pipeline end termination device a suspension force which is directed vertically upwards, - paying-out a first length of the pipe with the pipeline end termination device from the laying vessel vertically towards the seabed to a provisional anchoring position, in which the initial end length has an approximately vertical orientation with a vertical safety distance between the pipeline end termination device and the seabed, - extending a damping cable from the pipeline end termination device through the redirecting device to an underwater damping buoy, so that the damping cable, slidingly supported and redirected by the redirecting device and tensioned by a buoyancy force of the damping buoy, forms a damping provisional anchoring of the pipeline end termination device to the fixed receiving structure, - moving the laying vessel horizontally away from the fixed receiving structure and paying-out, from the laying vessel, a further length of the pipe so as to incline the initial end length progressively from the vertical orientation towards a horizontal orientation up to a lowered position, - with the initial end length in the lowered position, moving the laying vessel to positioning the initial end length in horizontal direction in a final abutment position with respect to said target position, then abutting the pipeline end termination device in the final abutment position, - during the steps of inclining to the lowered position and of horizontally positioning the initial end length: - using the suspension force of the suspension buoy to counterbalance at least part of the weight of the pipeline end termination device, - using the buoyancy force of the damping buoy to counterbalance a pulling force of the initial end length of the pipe and to damp the movements of the initial end length of the pipe, - using the sliding support of the redirected damping cable to allow relative compensation movements between the pipeline end termination device and the fixed receiving structure. - using the suspension force of the suspension buoy to counterbalance at least part of the weight of the pipeline end termination device, - using the buoyancy force of the damping buoy to counterbalance a pulling force of the initial end length of the pipe and to damp the movements of the initial end length of the pipe, - using the sliding support of the redirected damping cable to allow relative compensation movements between the pipeline end termination device and the fixed receiving structure.