The homotopy continuationmethods are useful tools for finding multiple solutionsof nonlinear problems.Animportant issue of this kind ofmethod is the correct implementationof the path-following techniques used to trace the homotopy trajectory. Therefore, in thiswork we propose a modification of the spherical algorithm to successfully trace the closedpaths of a DBH homotopy. The proposed methodology is depicted with three examples.Finally, a comparison of the results with a standard path-following technique is presentedand discussed.