the head portions 10 of the rail ends e are brought into contact with each other along their vertical end surfaces 14 further the end portions e are aligned so that the upper surfaces 60 of the head portions 10 are aligned in a common horizontal plane as the leveling joint l is being assembled in an installed leveling joint l a second joint body 140 is provided to be installed opposite the joint body 40 on right hand joints such as an inner side of the rails 20 and 22 where the two such rails are of different height the joint body 140 has like structural components to the joint body 40 but the relative location of the upper surface 48 and the lower surfaces 50 and 56 of segments 54 and 58 on joint body 140 are reversed from those of joint body 40 accordingly the joint body 140 is used on the inner side of a left hand joint and on the outer side of a right hand joint the leveling joint bodies 40 and 140 which are installed on opposite sides of end sections e of a rail joint according to the present invention are manufactured so that dimensions d 1 and.