LiPF3(CF2CF3)3 from Merck KGaA (LiFAP) was tested as a new electrolyte for Li-ion batteries that can replace the commonly used LiPF6. The latter salt is known to be unstable, to decompose thermally to LiF and PF5, and to readily undergo hydrolysis with protic species to form HF contamination in solutions. The latter contamination may have a detrimental impact on the performance of both anodes and cathodes for Li-ion batteries. Solutions comprising LiFAP, LiPF6, and LiN(SO2CF2CF3)2 (LiBETI) in mixtures of ethylene, dimethyl, and diethyl carbonates were tested with composite graphite and LiMn2O4 electrodes. The tools for this study included voltammetry (fast and slow scan rates), chronopotentiometry, impedance spectroscopy, Fourier transform infrared, and X-ray and photoelectron spectroscopies. It was found that LiFAP is superior to LiPF6 as an electrolyte for both graphite anodes and LiMn2O4 cathodes. This should be attributed to the different surface chemistry developed on these electrodes when LiPF6 is replaced by LiFAP. An important impact of such a replacement is probably the absence of possible pronounced HF contamination in LiFAP solutions.