Bose-Einstein correlations (BEC) of like-charge particle pairs are studied in e+e- -> W+W- hadronic decays recorded at centre-of-mass energies between 183 and 208 GeV with the OPAL detector at LEP. Using a recently proposed method which allows a search for BEC directly from the data, the possible existence of correlations between hadrons originating from different Ws in fully hadronic W+W- events is investigated. The results are compared to the Pythia Monte Carlo, in particular to predictions of its recent implementation of BEC effects.