Method for carrying out underwater drilling for underwater arranging an auxiliary connecting element, such as a line or chain, from a starting point through the seabed to an end point on the seabed, comprising the steps: - launching an underwater drilling device with a drilling unit including a drive unit and an alignment unit for aligning drill pipes, which alignment unit is adjustable at an angle (α) with respect to the seabed which drilling angle of the drilling unit is between at least 10° and at most 60° with respect to the seabed and which drilling unit is at least partly positioned within a substantially upwardly closed-off space having downwardly an opening e.g. a sea container having an at least partly open underside; - sinking the underwater drilling device down to the seabed; - positioning the underwater drilling device on the seabed; - placing the alignment unit of the underwater drilling device at a drilling angle (α); - drilling a drill passage at the drilling angle (α) from the starting point in the seabed with the aid of the drilling unit of the underwater drilling device using a first drill pipe which is provided with a controllable drill head; - steering the drill head through the seabed to the end point on the seabed; - observing the course of the drilling wherein during the drilling the starting point on the seabed is held substantially in an environment of a gaseous medium, such that the direct environment around the starting point on the seabed is kept substantially free from water and no or hardly any clouding of the direct environment around the starting point will occur, the course of the drilling being monitored by observing the starting point; - linking at the end point a reamer with an elongate flexible auxiliary connecting element to the drill pipe; - withdrawing the reamer with the auxiliary connecting element to the starting point on the seabed. - launching an underwater drilling device with a drilling unit including a drive unit and an alignment unit for aligning drill pipes, which alignment unit is adjustable at an angle (α) with respect to the seabed which drilling angle of the drilling unit is between at least 10° and at most 60° with respect to the seabed and which drilling unit is at least partly positioned within a substantially upwardly closed-off space having downwardly an opening e.g. a sea container having an at least partly open underside; - sinking the underwater drilling device down to the seabed; - positioning the underwater drilling device on the seabed; - placing the alignment unit of the underwater drilling device at a drilling angle (α); - drilling a drill passage at the drilling angle (α) from the starting point in the seabed with the aid of the drilling unit of the underwater drilling device using a first drill pipe which is provided with a controllable drill head; - steering the drill head through the seabed to the end point on the seabed; - observing the course of the drilling wherein during the drilling the starting point on the seabed is held substantially in an environment of a gaseous medium, such that the direct environment around the starting point on the seabed is kept substantially free from water and no or hardly any clouding of the direct environment around the starting point will occur, the course of the drilling being monitored by observing the starting point; - linking at the end point a reamer with an elongate flexible auxiliary connecting element to the drill pipe; - withdrawing the reamer with the auxiliary connecting element to the starting point on the seabed.