A machine for cleaning a ballast bed has, in front of a take-up device relative to a working direction, a first signal receiver—suitable for position determination in a global navigational satellite system—for scanning an actual track position. A second signal receiver connected to the machine for scanning a new track position created by laying down the raised track onto the re-applied ballast bed is arranged downstream. Both signal receivers are associated with a control device designed to act on the drives that displace a track-lifting device relative to the machine frame.