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We present the first model-independent measurement of the helicity of W bosons produced in top quark decays, based on a 1 fb-1 sample of candidate tt events in the dilepton and lepton plus jets channels collected by the D0 detector at the Fermilab Tevatron pp Collider. We reconstruct the angle Ө* between the momenta of the down-type fermion and the top quark in the W boson rest frame for each top quark decay. A fit of the resulting cosӨ* distribution finds that the fraction of longitudinal W bosons ƒ0 = 0.425 ± 0.166(stat) ± 0.102(syst) and the fraction of right-handed W bosons ƒ+ = 0.119 ± 0.090(stat) ± 0.053(syst), which is consistent at the 30% C.L. with the standard model.