The authors report new results from the Cryogenic Dark Matter Search (CDMS II) at the Soudan Underground Laboratory. Two towers, each consisting of six detectors, were operated for 74.5 live days, giving spectrum-weighted exposures of 34 kg-d for germanium and 12 kg-d for silicon targets after cuts, averaged over recoil energies 10100 keV for a WIMP mass of 60GeV/c(sub 2). A blind analysis was conducted, incorporating improved techniques for rejecting surface events. No WIMP signal exceeding expected backgrounds was observed. When combined with our previous results from Soudan, the 90% C.L. upper limit on the spin-independent WIMP-nucleon cross section is 1.6OE10(sub -43) cm(sub 2) from Ge, and 3OE10(sub -42) cm(sub 2) from Si, for a WIMP mass of 60GeV/c(sub 2). The combined limit from Ge (Si) is a factor of 2.5 (10) lower than our previous results, and constrains predictions of supersymmetric models.