A bicycle rim including an annular shaped element whose cross-section includes a box shape demarcated by an upper bridge and a lower portion having a lower bridge and side walls, the lower bridge or the side walls having holes distributed evenly and provided for the connection of the spokes, the holes and their immediate vicinity defining boring zones. The thickness of the walls constituted by the lower bridge and the side walls has a nominal value in the boring zones and a lower value than the nominal value in the intermediate zones located between two adjacent boring zones, and the thickness of this wall varies progressively from the nominal value to the lower value to the nominal value.