A conical intersection is a singular point in nuclear coordinate space. As a result of this singularity the parameters used to search for energy-minimized conical intersections, energy gradients, energy difference gradients, and coupling vectors vary irregularly along the search path. This it-regular variation precludes the efficient use of extrapolation procedures to speed convergence. This impediment may be overcome by the use of extrapolatable functions, that is, functions that vary smoothly along the search path. From a topographical perspective this approach amounts to walking along a path parallel to the ridge of conical intersections. In this work an algorithm based on these functions is introduced and its performance discussed.