  We present chemical abundances for the elements carbon, sodium, and fluorine
in 15 red giants of the globular cluster M 4, as well as six red giants of the
globular cluster $\omega$ Centauri. The chemical abundances were calculated in
LTE via spectral synthesis. The spectra analyzed are high-resolution spectra
obtained in the near-infrared region around $\lambda$2.3$\mu$m with the Phoenix
spectrograph on the 8.1m Gemini South Telescope, the IGRINS spectrograph on the
McDonald Observatory 2.7m Telescope, and the CRIRES spectrograph on the ESO
8.2m Very Large Telescope. The results indicate a significant reduction in the
fluorine abundances when compared to previous values from the literature for M
4 and $\omega$ Centauri, due to a downward revision in the excitation
potentials of the HF(1-0) R9 line used in the analysis. The fluorine abundances
obtained for the M 4 red giants are found to be anti-correlated with those of
Na, following the typical pattern of abundance variations seen in globular
clusters between distinct stellar populations. In M 4, as the Na abundance
increases by $\sim$+0.4 dex, the F abundance decreases by $\sim$-0.2 dex. A
comparison with abundance predictions from two sets of stellar evolution models
finds that the models predict somewhat less F depletion ($\sim$-0.1 dex) for
the same increase of +0.4 dex in Na.
