Observation of global states is of a great importance in the area of distributed systems monitoring. Global states constructed with the use of real time timestamps involve small communication and computational cost and therefore are suitable for monitoring large systems. Properties of Strongly Consistent Global States (SCGS) make them especially useful for on-line monitoring and direct application control. SCGS detection depends heavily on clock synchronization quality. This quality can be improved easily (or it is very good already) locally, within a subset of processes. A SCGS detection algorithm exploiting local fine synchronization is presented. It detects more states than a usual algorithm allowing for more strict control over a monitored application.