Australia Telescope Compact Array images of the giant radio galaxy PKS B1545-321 show a pair of oppositely directed beams emerging from a radio core and ending in bright components that are symmetrically located on either side. These inner beams are embedded within edge-brightened outer lobes of lower surface brightness, and the bright ends of the inner beams are well recessed from the ends of the outer lobes. The inner beams and diffuse surrounding lobes share a common central core and radio axis. We propose that the observed inner beams are double lobes that have been created within relic outer lobes as a consequence of a restarting of the central activity; therefore, PKS B1545-321 is a rare opportunity for examining the development of restarted beams within a relic synchrotron plasma cocoon. The inner double representing the new episode has among the highest axial ratios found in typical edge-brightened radio galaxies. The low radio luminosity of the inner double, the narrow and constant transverse extent of its cocoon, and the relatively low brightness of the hot spots at its ends are consistent with the almost ballistic propagation expected for a beam that has a low density contrast and is advancing within a relatively light ambient medium.