A radome for a concave-reflector antenna is fastened directly onto the reflector's edge. The inner surface of the radome comprises at least one absorbent part partially covering its surface area and disposed along its peripheral edge. The surface area of the radome covered by the absorbent part(s) is less than 15% of the total surface area. The radome may comprise two absorbent parts in diametrically opposite positions. Each absorbent part may have a substantially triangular shape, the base of the absorbent part being rounded along the radome's edge, and a portion of its surface area having been removed laterally from each side of the triangle in a circular arc cut-out.