A trenching assembly lays a continuous pipeline in a trench dug in a bed with uneven bathymetry, the trenching assembly including a trench digging device having a main body; at least four ground contact units, each unit having a height adjustment device, to position each ground contact unit with respect to the main body independently. A trench cutting tool digs in the bed includes a cutting depth adjustment device, for positioning the cutting tool with respect to the main body. A detection device detects bed bathymetry. A control device simultaneously allows cooperation between the detection device, the height adjustment device of each ground contact unit, and the cutting depth adjustment device. A command device cooperates with the control device to adjustment each ground contact unit and the cutting depth adjustment device, to obtain a trench having a height difference lower than a predefined tolerance and a predetermined burial depth.