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We present results of a search for WH → ℓνbb production in pp collisions based on the analysis of 1.05 fb-1 of data collected by the D0 experiment at the Fermilab Tevatron, using a neural network for separating the signal from backgrounds. No signal-like excess is observed, and we set 95% C.L. upper limits on the WH production cross section multiplied by the branching ratio for H → bb for Higgs boson masses between 100 and 150 GeV. For a mass of 115 GeV, we obtain an observed (expected) limit of 1.5 (1.4) pb, a factor of 11.4 (10.7) times larger than the standard model prediction.