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When the forwarding paths in an IP network change due to a link failure or a link weight modification, the forwarding tables in the routers may need to be updated. Each of these updates may cause transient loops if they are not performed in an appropriate order. In this paper, we propose an order to update the forwarding tables that avoids transient loops for non-urgent changes. The order is obtained by studying the changes in the forwarding tables, therefore it can be used in networks running any routing protocols, and for any type of forwarding path changes. After presenting the order, we prove that it is correct, and present an efficient algorithm to compute the order. Thereafter, we present several algorithms for performing forwarding table updates in accordance with the order. We also discuss how the update algorithms can be applied to both networks with centralized control and decentralized routing protocols. Finally, we study the update algorithms' performance on several network topologies and with varying parameter settings and for several types of forwarding path changes.