We address the symmetric flip problem that is inherent to multi-resolution isometric shape matching algorithms. To this effect, we extend our previous work which handles the dense isometric correspondence problem in the original 3D Euclidean space via coarse-to-fine combinatorial matching. The key idea is based on keeping track of all optimal solutions, which may be more than one due to symmetry especially at coarse levels, throughout denser levels of the shape matching process. We compare the resulting dense correspondence algorithm with state-of-the-art techniques over several 3D shape benchmark datasets. The experiments show that our method, which is fast and scalable, is performance-wise better than or on a par with the best performant algorithms existing in the literature for isometric (or nearly isometric) shape correspondence. Our key idea of tracking symmetric flips can be considered as a meta-approach that can be applied to other multi-resolution shape matching algorithms, as we also demonstrate by experiments.