An algorithm is described for tagging the flavour content at production of neutral B mesons in the LHCb experiment. The algorithm exploits the correlation of the flavour of a B meson with the charge of a reconstructed secondary charm hadron from the decay of the other b hadron produced in the proton-proton collision. Charm hadron candidates are identified in a number of fully or partially reconstructed Cabibbo-favoured decay modes. The algorithm is calibrated on the self-tagged decay modes B+ -> J/psi K+ and B-0 -> J/psi K*(0) using 3.0fb(-1) of data collected by the LHCb experiment at pp centre-of-mass energies of 7TeV and 8TeV. Its tagging power on these samples of B -> J/psi X decays is (0.30 +/- 0.01 +/- 0.01) %
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