Context : Aims : We describe the discovery of an extremely wide pair of low-mass stars with a common large proper motion and discuss their possible membership in a Galactic halo stream crossing the Solar neighbourhood . Methods : In a high proper motion survey of the southern sky we used multi-epoch positions and photometry from the SuperCOSMOS Sky Surveys . New nearby ultracool dwarf and subdwarf candidates were selected among the faint and red high proper motion objects , and subsequently confirmed by low-resolution classification spectroscopy . The resulting spectroscopic distance estimates , approximate radial velocity measurements and improved proper motions involving additional epochs from the Two Micron All Sky Survey and from the DEep Near-Infrared Survey were used to compute Galactic space velocities . Results : The late-type ( M7 ) dwarf SSSPM J2003 - 4433 and the ultracool subdwarf SSSPM J1930 - 4311 ( sdM7 ) sharing the same very large proper motion of about 860 mas/yr were found in the same sky region with an angular separation of about 6° . From the comparison with other high proper motion catalogues we have estimated the probability of a chance alignment of the two new large proper motions to be less than 0.3 % . From the individually estimated spectroscopic distances of about 38 ^ { +10 } _ { -7 } pc and 72 ^ { +21 } _ { -16 } pc , respectively for the M7 dwarf and the sdM7 subdwarf , and in view of the accurate agreement in their large proper motions we assume a common distance of about 50 pc and a projected physical separation of about 5 pc . The mean heliocentric space velocity of the pair ( U,V,W ) = ( -232 , -170 , +74 ) km/s , based on the correctness of the preliminary radial velocity measurement for only one of the components and on the assumption of a common distance and velocity vector , is typical of the Galactic halo population . Conclusions : The large separation and the different metallicities of dwarfs and subdwarfs make a common formation scenario as a wide binary ( later disrupted ) improbable , although there remains some uncertainty in the spectroscopic classification scheme of ultracool dwarfs/subdwarfs so that a dissolved binary origin can not be fully ruled out yet . It seems more likely that this wide pair is part of an old halo stream . Higher-resolution spectroscopic observations are needed to measure accurate radial velocities of both components . Further , we suggest to check the M7 dwarf for an unresolved binary status , which would explain its shorter spectroscopic distance estimate , and to place both objects on a trigonometric parallax program .