Gridded digital elevation data, often referred to as DEMs, are one of the most widely available forms of environmental data. Topographic analysis of DEMs can take many forms, but in hydrologic and geomorphologic applications it is typically used as a surrogate for the spatial variation of hydrological conditions (topographic indices) and flow routing. Here we report on a new flow routing algorithm and compare it to three common classes of algorithms currently in widespread use. The advantage of the new algorithm is that unrealistic dispersion on planar or concave hillslopes is avoided, whereas multiple flow directions are allowed on convex hillslopes. We suggest that this new triangular multiple flow direction algorithm (MD∞) is more appropriate for a range of flow routing and topographic index applications.