A search for the lepton-flavour violating decay cc45" title="Click to view the MathML source">D0→e±μ∓ is made with a dataset corresponding to an integrated luminosity of accfdc386158ce9873498f288901"> of proton–proton collisions at centre-of-mass energies of and ace21c4d45fb036fe0c92757049a">, collected by the LHCb experiment. Candidate D0 mesons are selected using the decay D⁎+→D0π+ and the cc45" title="Click to view the MathML source">D0→e±μ∓ branching fraction is measured using the decay mode acf2c2ba49be9507581c6d97f5c66b" title="Click to view the MathML source">D0→K−π+ as a normalization channel. No significant excess of cc45" title="Click to view the MathML source">D0→e±μ∓ candidates over the expected background is seen, and a limit is set on the branching fraction, B(D0→e±μ∓)<1.3×10−8, at 90% confidence level. This is an order of magnitude lower than the previous limit and it further constrains the parameter space in some leptoquark models and in supersymmetric models with R-parity violation.