Rim for cycle wheel and method for manufacturing same

The rim (3) has a lateral flange (5a) and another lateral flange located on respective sides of a median plane of the rim. Each flange comprises an outer surface (S5a) facing away from the median plane. A bridge (6) connects the flanges to one another and comprises an outer surface facing an axis of rotation of a cycle wheel. A middle zone of the outer surface of the bridge has a transverse width, measured perpendicular to the median plane, greater than 4 mm. The middle zone is machined over 95, 97 or 100 percent of circumference of the rim. An independent claim is also included for a method for manufacturing a rim for a cycle wheel.