A method approximates and connects an off shore riser duct to a floating unit, includes installing a tubular coupling recipient on the floating unit at a riser coupling level, the coupling recipient having an annular side wall extending around a longitudinal axis. A pulling device is on the floating unit at a pulling device level above the riser coupling level. The pulling device pulls a line extended through the coupling recipient and connected to a pulling head at a riser duct upper end. The riser duct upper end is pulled into the coupling recipient, providing a locking mechanism to lock a coupling adapter against downward withdrawal. Extending the line along a curved deviating surface deviates the pulling direction. The curved deviating surface is formed by a deviating member connected to the coupling recipient at a distance from the longitudinal axis smaller than an annular side wall to longitudinal axis distance.