We predict battery voltages close to 6 V when LiCaCoF6 or LiCdCoF6 are used as cathode materials based on our first principles band-structure calculations. Although these fluorides use the same redox reaction as that of LiCoO2/CoO2, i.e., Co3+/Co4+, the fluorides are expected to show approximately 2 V greater voltages. This may be simply explained by the greater electronegativity of fluorine than oxygen; thereby the redox potential of Co3+/Co4+ can be better utilized. Theoretical volume changes associated with the delithiation of these fluorides are estimated to be +0.4 and -2.5%, which may be advantageous in achieving a long cycle lifetime. A series of fluorides, LiACoF(6) with A(2+) and Co3+ ions, can be expected to show similar voltages. Thus the materials can be optimized according to other properties such as lithium mobility.