[en] The EDELWEISS experiment has improved its sensitivity for the direct search for WIMP dark matter. In the recoil energy range relevant for WIMP masses below 10 TeV/c², no nuclear recoil were observed in the fiducial volume of a heat-and-ionization cryogenic Ge detector operated in the low-background environment of the Laboratoire Souterrain de Modane in the Frejus Tunnel, during an effective exposure of 7.4 kg·d. This result is combined with the previous EDELWEISS data to derive a limit on the cross-section for spin-independent interaction of WIMPs and nucleons as a function of WIMP mass, using standard nuclear physics and astrophysical assumptions. This limit excludes at more than 99.8% CL a WIMP candidate with a mass of 44 GeV/c² and a cross-section of 5.4 x 10^-6 pb, as reported by the DAMA collaboration. A first sample of supersymmetric models are also excluded at 90% CL. (authors)