In the context of the IEEE 1588 Precision Time Protocol (PTP), estimating the delay's bias is a problem that appears in both one-way (using transparent devices) or two-way message exchange mechanisms. For estimating the offset via the two-way message exchange mechanism, it is usually being assumed that the expected value of delays in forward and reverse directions are equal with each other. However this is not a realistic assumption for packet-based wide area networks, where delays in down-link and up-link directions may have a significant difference. In this work we propose a solution to estimate the random delay's bias and improve the synchronization accuracy of IEEE 1588. Our method is easy to implement and is compatible with the current version of the protocol. In addition to the improvement in synchronization accuracy, our method allows us to update the slave clock recursively.