Using a sample of 213 713 stars from the Radial Velocity Experiment (RAVE) survey, limited to a distance of 2 kpc from the Sun and to |z| < 1 kpc, we report the detection of a velocity gradient of disc stars in the fourth quadrant, directed radially from the Galactic Centre. In the direction of the Galactic Centre, we apply a simple method independent of stellar proper motions and of Galactic parameters to assess the existence of this gradient in the RAVE data. This velocity gradient corresponds to |K+C| > rsim 3 km s−1 kpc−1, where K and C are the Oort constants measuring the local divergence and radial shear of the velocity field, respectively. In order to illustrate the effect, assuming a zero radial velocity of the local standard of rest we then reconstruct the two-dimensional Galactocentric velocity maps using two different sets of proper motions and photometric distances based either on isochrone fitting or on K-band magnitudes, and considering two sets of values for the Galactocentric radius of the Sun and local circular speed. Further observational confirmation of our finding with line-of-sight velocities of stars at low latitudes, together with further modelling, should help constrain the non-axisymmetric components of the Galactic potential, including the bar, the spiral arms and possibly the ellipticity of the dark halo.