We have measured the W transverse momentum distribution (pTW) using a sample of 323 W → eν and W → μν events produced in proton-antiproton collisions at the CERN collider. In the present letter we extend the study of the distribution up to pTW ∼- m W and compare to leading and higher order QCD. This comparison is a precise test of QCD with hadron colliders and the inclusive spectrum gives good agreement over a large range of pTW. However we observed two events at very large pTW (∼- 100 GeV/c) in which the W candidate recoils against an energetic di-jet system. Both events have a very large missing transverse energy and a jet-jet mass compatible with the W mass. In a separate analysis, a topologically similar event has been observed in which a high-mass di-jet system is balanced by a large missing transverse energy which could be interpreted as Z0 → νν decay. We cannot easily explain these three events in terms of explicit second-order QCD calculations. However we cannot exclude at this stage the possibility that they are the result of non-gaussian fluctuations in the response of UA1 calorimetry or a statistical fluctuation in the data.