Despite years of research, the Internet still lacks a routing protocol with guaranteed termination. As is well-known, decentralization of routing decisions among the Autonomous Systems (ASes) that comprise the Internet may result in permanent oscillations of the state of its routing protocol - the Border Gateway Protocol (BGP). Some permanent oscillations are made from routing loops - the propagation of routing messages around the cycles of a network - that come back time and again. We discovered that the routing loop detection capability of BGP can be sharpened to predict which routing loops potentially recur and that the import policies can be adjusted to prevent the recurrence. The resulting protocol, named Self-Stable BGP (SS-BGP), is more stable than BGP. For the broad and common class of isotone routing policies, all permament oscillations are made from recurrent routing loops. For this class of routing policies, SS-BGP terminates. Our simulations with realistic Internet topologies and realistic variations of the Gao-Rexford (GR) inter-AS routing policies show that SS-BGP arrives at stable states at the expense of alterations in the import policies of only a handful of ASes.