Over a two-year period, Voyager 1 observed a gradual slowing-down of radial plasma flow in the heliosheath to near-zero velocity after April 2010 at a distance of 113.5 astronomical units from the Sun (1 astronomical unit equals 1.5 × 10(8) kilometres). Voyager 1 was then about 20 astronomical units beyond the shock that terminates the free expansion of the solar wind and was immersed in the heated non-thermal plasma region called the heliosheath. The expectation from contemporary simulations was that the heliosheath plasma would be deflected from radial flow to meridional flow (in solar heliospheric coordinates), which at Voyager 1 would lie mainly on the (locally spherical) surface called the heliopause. This surface is supposed to separate the heliosheath plasma, which is of solar origin, from the interstellar plasma, which is of local Galactic origin. In 2011, the Voyager project began occasional temporary re-orientations of the spacecraft (totalling about 10-25 hours every 2 months) to re-align the Low-Energy Charged Particle instrument on board Voyager 1 so that it could measure meridional flow. Here we report that, contrary to expectations, these observations yielded a meridional flow velocity of +3 ± 11 km s(-1), that is, one consistent with zero within statistical uncertainties.