A rim base to be used with the rim of a wheel, particularly the rim of a so-called box section bicycle rim, as well as a rim equipped with such a rim base, and a wheel having such rim and rim base. The rim base is formed by a continuous annular strip having, in cross section, a median depression, forming a U-shaped radial groove provided to be positioned within in the central well of the rim, two lateral extensions provided to be supported upon on the interior edges of the rim that border of the well, and two lateral walls provided to extend along the flanges of the rim. The walls of the rim base are extended by a pair of lips that project toward the inside relative to the walls of the rim base, the lips being adapted to be positioned adjacent the lips of the rim.