  In a recent study by Dittmar and Dreiner it was shown that with appropriate
selection cuts the signature of events containing two charged leptons and
missing energy represents the best chance of detecting the Standard Model Higgs
scalar in the mass range between 155 and 180 GeV, the primary decay of the
Higgs being into pairs of charged gauge bosons. The largest background to this
channel is due to irreducible $W^+W^-X$ production. In the present paper we
calculate the contribution of events of the type $bg\to tW^\pm\to b W^+W^-\to b
\ell^{+}\ell^{'-}\nu_\ell\bar\nu_{\ell'}$, which have not been considered yet
within the new selection strategy. We show that the yield of this background is
rather large, at the level of that produced by $W^+W^-$, $t\bar t$ or $tb
W^\pm$ events and thus needs to be incorporated in future experimental
analyses. However, we find that its inclusion will not spoil the possibilities
of Higgs detection in the above mentioned channel at the Large Hadron Collider.
