The motion of phospholipids has previously been studied on many time scales due to the significance for living cells and technological applications. The motions on a pico- to nanosecond time scale were determined by quasielastic neutron scattering (QENS) to be much faster than the ones on the microsecond scale covered by fluorescence recovery after photobleaching (FRAP). This was explained by assuming that the molecules rattle fast in a cage of neighbors (observed with QENS) from which they escape once in a while; this escape was then the primary step of the slower diffusion measured by FRAP. However, nanosecond MD simulation studies could not observe any escape events; recent findings even suggested that the long-range motion in phospholipid membranes on short time scales is not diffusive but has flow-like characteristics. To check this novel view, we have repeated the QENS experiments with today's significantly improved instrumentation. By using the advantage of QENS that allows tuning of the observation time in the pico- to nanosecond range, it was possible to study the evolution of motions in this time frame. Localized motions, e.g., of the head and tail groups, appear separated from the long-range motion and do not obfuscate the analysis as they do in a mean squared displacement plot. The results for the long-range motion are indeed compatible with flow patterns, whereas the localized motions can account for the fast motions interpreted as motions in a cage before. Hereby, we give experimental evidence for a completely different mechanism of long-range motion on short time scales in phospholipid membranes.