The aim of the present invention is a sub-reflector of a dual-reflector antenna comprising:a first end having a junction of a first diameter, adapted for coupling to the end of a waveguide,a second end, having a second diameter greater than the first diameter,a convex reflective internal surface placed at the second end having an axis of revolution,an external surface of the same axis, joining the two ends,a dielectric material extending between the first and the second ends and limited by the internal surface and the external surface,In accordance with the invention, the external surface has a convex profile described by a polynomial equation of the sixth degree of the formula:y=ax6+bx5+cx4+dx3+ex2+fx+g where a is not zero.