The well-known black hole X-ray transient A0620-00 was a bright radio source during the first part of its outburst in 1975. We have revisited the available data and find for the first time evidence that the source exhibited multiple jet ejections. Rapid radio spectral changes indicate the addition of at least three new components, which are initially optically thick. From single-baseline interferometry taken about three weeks after the start of the X-ray outburst, we find that the source is extended on arcsec scales and infer a relativistic expansion velocity. Some of the other (soft) X-ray transients, such as GS 1124-68 and GS 2000+25, show very similar X-ray outburst light curve shapes to that of A0620-00, while their radio outburst light curve shapes are different. We suggest that this is caused by the radio emission being strongly beamed in outburst, whereas the X-ray emission remains isotropic. As this effect is stronger at higher jet velocities, this strengthens our conclusion that the jets in A0620-00 and other soft X-ray transients move with relativistic speeds.