A coupling antenna which includes a plurality of turns in series located on a planar support (14) formed by an insulating dielectric substrate. The antenna includes one or several sets of at least one turn (16) located on the planar support, mounted in series, at least one of the sets consisting of at least two spires (16,22) in series superposed along an axis perpendicular to the plane of the support and separated by an insulating strip (20) of dielectric ink, thereby resulting in a high inductance value. The invention also concerns the method for making such an antenna and the use of the antenna in a contactless smart card.