The fundamental inverse problem in distance geometry is the one of finding positions from inter-point distances. The {\it discretizable molecular distance geometry problem} (DMDGP) is a subclass of the {\it distance geometry problem} (DGP) whose search space can be discretized and given by a binary tree, which can be explored by a {\it branch@-and@-prune} (BP) algorithm. Moreover, it can be seen that this combinatorial search space possesses many interesting symmetry properties studied in the last ten years. \par In this research, the authors present a new algorithm for this subclass of DGP, which exploits DMDGP symmetries more effectively than its predecessors. Finally, computational results indicate that the speedup, with respect to the classic BP algorithm, is considerable for sparse DMDGP instances related to protein conformation.