Half grabens and supra-detachment basins correspond to end-member basin types of magma-poor rift settings, each of them showing a characteristic stratigraphic architecture. The occurrence of a basement-cover décollement has been shown to drastically change the stratigraphic architecture of half graben basins, however, the effect of such basement-cover décollement remains to be documented in supra-detachment basins formed during hyper-extension. We investigate the tectono-stratigraphic record of the Arzacq Basin (SW France) recording the formation of a salt-rich Cretaceous hyperextended rift system. Combining 2-D and 3-D seismic reflection calibrated from well data, we show that this basin is an asymmetric syn-rift extensional syncline growing above a pre-kinematic salt layer. By mapping the sub-salt basement, we show that the formation of this syncline is controlled by the South-Arzacq Fault (SAF), soling in the sub-salt basement. Based on crosscutting relationships and the observed southward migration of syn-rift depocenters, this N110°-striking, 20°-dipping structure accommodates >10 km of thick-skinned extension. The overlying supra-salt cover coherently glided, following the basement geometry. The 3-D segmentation of the SAF and the sub-salt stratigraphic architecture of the Arzacq Basin suggest a roughly dip-slip kinematic. A post-kinematic kilometer-scale uplift is documented on the southern side of the Arzacq Basin. It may result from the increasing lithospheric thinning and thermal support at the end of asymmetric hyperextension. As salt commonly occurs in extensional settings, we believe that our description of the tectono-stratigraphic record of a basement-decoupled supra-detachment basin has global applicability to unleash the tectono-stratigraphic evolution of worldwide hyper-extended rifted margins.