We present a measurement of the W boson mass in W-->e(nu) decays using 1 fb-1 of data collected with the D0 detector during Run II of the Fermilab Tevatron collider. With a sample of 499830 W-->e(nu) candidate events, we measure M(W)=80.401+/-0.043 GeV. This is the most precise measurement from a single experiment.