We demonstrate a method of preparation of broadband sign-reversible dispersion in alkali vapour based on velocity-selective optical pumping. The refractive index in Rb vapour has been measured using a heterodyne method. The magnitudes of the normal and anomalous dispersion, which are almost constant over a spectral region of approximately 40 MHz, can lead to a reduced (V(g) approximately c/230) or negative (V(g) approximately -c/27) group velocity of light.