A device for transferring fluid between two floating supports anchored to the sea bottom, having a rigid central undersea pipe installed below the surface with its ends each being connected to respective ones of two supports via a flexible hose. The main portion of the rigid central pipe includes or co-operates with buoyancy elements such that the central pipe adopts, in a quasi-static rest state, a configuration of an arch, preferably following a curve such that the angles between the half-lines of the axes of the rigid pipe and the horizontal half-lines at each of its ends extending towards the other end present absolute values of less than 20° and the flexible hoses present lengths and curvatures such that variations in the curvatures of the flexible hoses are suitable for compensating the movements of the floating supports.