A third-degree polynomial expansion of the potential function of CF 4 has been fitted directly to the experimental transition frequencies, without the use of a contact transformation or the usual spectroscopic constants. The principle of the calculation from the potential to the frequencies was described preciously ( J. Mol. Spectrosc.126, 405-426 (1987)). The least-squares fitting is carried out through a singular value decomposition of the matrix of the system of conditional equations. Generally the recalculated transition frequencies fit the observed ones to about 0.1 cm -1 for IR and Raman lines and within a few percent for pure rotational transitions. The deviation of the fit is shown graphically. The recalculated energies correctly reproduce a complicated resonance between the fundamental ν3 state and the 2 ν4 state, including the pattern of 6-fold, 8-fold, and 12-fold clusters. Because of the low number of constants used in the model, the obtained potential function is well suited for extrapolations and for assignment purposes.