The observation that a moving clock runs slow is usually observed by a set of spatially separated, co-moving and synchronized clocks. The synchronization of these co-moving and spatially separated clocks is achieved by the Einsteinian synchronization convention. The universal validity of this convention has been debated by researchers for over a hundred years. In this paper we present the Doppler Effect as a phenomenon to eliminate the issues associated with the synchronization problem. The Doppler Effect involves two objects, the light source and the receptor in relative motion. The ratio of the frequencies expected to be observed by the receptor as estimated by the inertial frames co-moving with the source and the receptor respectively is (1-v2/c2), assuming that light travels at speed c in all directions with respect to the source and receptor respectively. The relativistic prediction is the geometric mean of these two estimates. The inertial frame co-moving with the source reconciles this difference by stating that the clock at the location of the moving receptor is running slow by a factor (1-v2/c2)1/2. A similar explanation is given by the inertial frame co-moving with the receptor – the clocks at the location of the moving source run slow by a factor (1-v2/c2)1/2, that is the actual emission frequency is less than what the source of light itself observes, due to the slow running of the clock co-moving with the source. Thus the relativistic Doppler Effect is reconciled with the predictions of the individual inertial frames by the slow running of moving clocks. This essentially means that moving clocks run slow – even when we do not use the Einsteinian synchronization convention and use the opportunity presented by the Doppler Effect to observe a ‘moving’ clock by a ‘stationary’ clock, assuming that the speed of light is c in all directions. This essentially means that a moving clock actually runs slow as compared to the usual statement that a ‘moving’ clock is observed to run slow (by ‘stationary’, spatially separated and synchronized (by a convention) clocks). The consequence of the actual slow running of moving clocks is discussed in the conclusion section.