Paths with loops, even transient ones, pose significant stability problems in networks. As a result, much effort has been devoted over the past thirty years to designing distributed algorithms capable of avoiding loops. We present a new algorithm, Distributed path computation with Intermediate Variables (DIV), that guarantees that no loops, transient or steady-state, can ever form. DIV’s novelty is in that it is not restricted to shortest paths, can easily handle arbitrary sequences of changes and updates, and provably outperforms earlier approaches in several key metrics. In addition, when used with distance-vector style path computation algorithms, DIV also prevents counting-to-infinity; hence further improving convergence. The paper introduces DIV and its key properties. Simulation quantifying its performance gains are also presented.