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We present the first measurement of the electron angular distribution parameter α2 in W→eν events produced in proton-antiproton collisions as a function of the W boson transverse momentum. Our analysis is based on data collected using the DØ detector during the 1994–1995 Fermilab Tevatron run. We compare our results with next-to-leading order perturbative QCD, which predicts an angular distribution of (1 ± α1cos θ*+ α2 cos2 θ*), where θ* is the polar angle of the electron in the Collins-Soper frame. In the presence of QCD corrections, the parameters a1 and a2 become functions of pTW, the W boson transverse momentum. This measurement provides a test of next-to-leading order QCD corrections which are a nonnegligible contribution to the W boson mass measurement.