Using 1000BASE-T Ethernet for data acquisition with all clients connecting to the same switch, the 125Mhz Ethernet clock recovered by each client can serve as the shared synchronous clock. In order to synchronize the time stamp counters of the clients, we used special synchronizing broadcast messages. However, using these broadcast packets did not perfectly synchronize the time stamp values: a systematic offset and some random “jitter” remained. In our present paper we describe an algorithm that eliminates the non-deterministic part of the time stamp offset approximating the theoretical 8 ns accuracy. Our algorithm is based on identifying the left-edge of the client Packet Delay histogram and capable of aligning the client times with an accuracy of 16 ns. The reliability of the method was tested and proved by a long term measurement.