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HR 6819 was recently proposed to be a triple system consisting of an inner B-type giant + black hole binary with an orbital period of 40d and an outer Be tertiary. This interpretation is mainly based on two inferences: that the emission attributed to the outer Be star is stationary, and that the inner star, which is used as mass calibrator for the black hole, is a B-type giant. We re-investigate the properties of HR 6819 by spectral disentangling and an atmosphere analysis of the disentangled spectra to search for a possibly simpler alternative explanation for HR 6819. Disentangling implies that the Be component is not a static tertiary, but rather a component of the binary in the 40-d orbit. The inferred radial velocity amplitudes imply an extreme mass ratio of M_2/M_1 = 15 +/- 3. We infer spectroscopic masses of 0.4$^{+0.3}_{-0.1}$ Msun and 6$^{+5}_{-3}$ Msun for the primary and secondary, which agree well with the dynamical masses for an inclination of i = 32 deg. This indicates that the primary might be a stripped star rather than a B-type giant. Evolutionary modelling suggests that a possible progenitor system would be a tight (P_i ~ 2d) B+B binary system that experienced conservative mass transfer. While the observed nitrogen enrichment of the primary conforms with the predictions of the evolutionary models, we find no indications for the predicted He enrichment. We suggest that HR 6819 is a binary system consisting of a stripped B-type primary and a rapidly-rotating Be star that formed from a previous mass-transfer event. In the framework of this interpretation, HR 6819 does not contain a black hole. Interferometry can distinguish between these two scenarios by providing an independent measurement of the separation between the visible components.