A search for pair-produced charged Higgs bosons was performed in the data collected by the DELPHI detector at LEP II at centre-of-mass energies from 189 GeV to 209 GeV. Five different final states, , , , and were considered, accounting for the major expected decays in type I and type II Two Higgs Doublet Models. No significant excess of data compared to the expected Standard Model processes was observed. The existence of a charged Higgs boson with mass lower than 76.7 GeV/c2 (type I) or 74.4 GeV/c2 (type II) is excluded at the 95% confidence level, for a wide range of the model parameters. Model independent cross-section limits have also been calculated.