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| { { } _ { > } \atop { { } ^ { \sim } } } 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 .