Predicting latency between nodes on the internet can have a significant impact on the performance of many services that use latency distances among nodes as a decision making input. Coordinate-based approaches are among the family of latency prediction techniques where latency between each pair of nodes is modeled as the virtual distance among those nodes over a virtual system. This article proposes the Decentralized Coordinate System (DCS) as a fully distributed system that does not rely on any infrastructure support from the underlying network. DCS uses a two-phase algorithm: first, each host is assigned rough coordinates, then, the rough estimation is refined in a way that it gradually converges to the accurate relative position of nodes. Simulation results demonstrate that the accuracy of DCS is competitive with existing network coordinate systems and that it can be considered as a good alternative for some applications.