The invention relates to a cup member of a foldable furniture hinge, provided with two rotary fastening elements. To fasten it, it provides a radially extending retaining wing (1a, 1b) on each side of a longitudinal axis of the hinge, which resides radially on the inner side of a contour of a respective receiving blind hole in a non-installed state of the hinge and on the outer side thereof in an installed state. According to the present invention, the wing (1a, 1b) is positioned under a specific angle with respect to a cup element in order to obtain a smooth arcuate path of moving of a tip portion of said wing relatively to said stationary cup element, when incorporating, said path thus approaching to the outer surface of said furniture panel i.e. in a direction contrary to the direction of tightening the respective cup member. Said wing (1a, 1b) mates in an abutting manner a supporting face (4) of a cup core. Two supporting faces (4) reside in a common plane that forms an acute angle (α) with the surface plane of the furniture panel, with a tip thereof lying on the side of the cup member averted from the hinge arm (R).