Improved measurement of /V(cb)/ using B-->D*l nu decays.

We determine the weak coupling /V(cb)/ between the b and c quarks using a sample of 3 x 10(6) BB; events in the CLEO detector at the Cornell Electron Storage Ring. We determine the yield of reconstructed B-->D*l nu; decays as a function of w, the boost of the D* in the B rest frame, and from this we obtain the differential decay rate d Gamma/dw. By extrapolating d Gamma/dw to w=1, the kinematic end point at which the D* is at rest relative to the B, we extract the product /V(cb)/F(1), where F(1) is the form factor at w=1. Combined with theoretical results for F(1) we determine /V(cb)/=0.0469+/-0.0014(stat)+/-0.0020(syst)+/-0.0018(theor).