How to find a Higgs Boson with a Mass between 155--180 GeV at the LHC

We reconsider the signature of events with two charged leptons and missing energy as a signal for the detection of the Standard Model Higgs boson in the mass region M(Higgs)=155--180 GeV. It is shown that a few simple experimental criteria allow to distinguish events originating from the Higgs boson decaying to H --> W+W- from the non resonant production of W+W- X at the LHC. With this set of cuts, signal to background ratios of about one to one are obtained, allowing a 5--10 sigma detection with about 5~fb-1 of luminosity. This corresponds to less than one year of running at the initial lower luminosity L= 10**33/ cm**2/sec. This is significantly better than for the hitherto considered Higgs detection mode H --> Z Z* --> l+ l+ l- l-, where in this mass range about 100~fb-1 of integrated luminosity are required for a 5 sigma signal.