The 7Be(p,gamma)8B reaction plays a central role in the evaluation of solar neutrino fluxes. We report on a new precision measurement of the cross section of this reaction, following our previous experiment with an implanted 7Be target, a raster-scanned beam, and the elimination of the backscattering loss. The new measurement incorporates a more abundant 7Be target and a number of improvements in design and procedure. The point at E(lab)=991 keV was measured several times under varying experimental conditions, yielding a value of S17(E(c.m.)=850 keV)=24.0+/-0.5 eV b. Measurements were carried out at lower energies as well. Because of the precise knowledge of the implanted 7Be density profile, it was possible to reconstitute both the off- and on-resonance parts of the cross section and to obtain from the entire set of measurements an extrapolated value of S17(0)=21.2+/-0.7 eV b.