Context : G39 - 27/289 is a common proper motion pair formed by a white dwarf ( WD0433 + 270 ) and a main-sequence star ( BD + 26 730 ) that apparently has been classified as a member of the Hyades open cluster . Previous studies of the white dwarf component yielded a cooling time of \sim 4 Gyr . Although it has not been pointed out before explicitly , this result is 6 times larger than the age of the Hyades cluster , giving rise to an apparent conflict between the physics of white dwarfs and cluster main-sequence fitting . Aims : We investigate whether this system belongs to the Hyades cluster and , accordingly , give a plausible explanation to the nature of the white dwarf member . Methods : We have performed and analyzed spectroscopic observations to better characterize these objects , and used their kinematic properties to evaluate their membership to the Hyades . Then , different mass-radius relations and cooling sequences for different core compositions ( He , C/O , O/Ne and Fe ) have been employed to infer the mass and cooling time of the white dwarf . Results : From kinematic and chemical composition considerations we believe that the system was a former member of the Hyades cluster and therefore has an evolutionary link with it . However , the evidence is not conclusive . With regards to the nature of the white dwarf component , we find that two core compositions — C/O and Fe — are compatible with the observed effective temperature and radius . These compositions yield very different cooling times of \sim 4 Gyr and \sim 1 Gyr , respectively . Conclusions : We distinguish two posssible scenarios . If the pair does not belong to the Hyades cluster but only to the Hyades stream , this would indicate that such stream contains rather old objects and definitely not coeval with the cluster . This has interesting consequences for Galactic dynamics . However , our favoured scenario is that of a white dwarf with a rather exotic Fe core , having a cooling time compatible with the Hyades age . This is a tantalizing result that would have implications for the thermonuclear explosion of white dwarfs and explosion theories of degenerate nuclei .