Distributed routing algorithms may give rise to transient loops during path recomputation, which can pose significant stability problems in high-speed networks. We present a new algorithm, Distributed Path Computation with Intermediate Variables (DIV), which can be combined with any distributed routing algorithm to guarantee that the directed graph induced by the routing decisions remains acyclic at all times. The key contribution of DIV, besides its ability to operate with any routing algorithm, is an update mechanism using simple message exchanges between neighboring nodes that guarantees loop-freedom at all times. DIV provably outperforms existing loop-prevention algorithms in several key metrics such as frequency of synchronous updates and the ability to maintain paths during transitions. Simulation results quantifying these gains in the context of shortest path routing are presented. In addition, DIV's universal applicability is illustrated by studying its use with a routing that operates according to a non-shortest path objective. Specifically, the routing seeks robustness against failures by maximizing the number of next-hops available at each node for each destination.