(Li2MMF8)-M-II-F-IV compounds have been suggested as good fluorine conductors, based on their crystalline structure. A careful experimental investigation using several techniques, including ac and de electrical conductivity, calorimetric and Raman scattering measurements carried out on a Li2CaHfF8 crystal, leads us to propose a different structure for these compounds. This structure is compatible with the ionic conductivity and thermal behavior of our system. Also, piezoelectric resonances and Raman selection rules confirm our proposed non-centrosymmetrical group. A set of conduction mechanisms that describes the high anisotropic conductivity in the crystal is proposed.