  The origin and evolution of fluorine in the Milky Way galaxy is still in
debate. In particular, the increase of the [F/Fe] in metal-rich stars found
from near-IR HF-lines is challenging to explain theoretically. We determine the
fluorine abundances from 50 M giants in the solar neighbourhood spanning a
broad range of metallicities (-0.9<[Fe/H]<0.25 dex). These stars are cool
enough to have an array of HF lines in the K band. We observed the stars with
the IGRINS and investigate each of ten HF molecular lines in detail. Based on a
detailed line-by-line analysis of ten HF lines, we find that the R19, R18 and
R16 lines should primarily be used for abundance analysis. The R15, R14 and R13
lines can also be used, but the trends based on these lines show increasing
dependencies with the stellar parameters. The strongest HF lines, namely R12,
R11, R9 and R7 should be avoided since the abundances from them show
significant trends with the stellar parameters, and a high sensitivity to
variations in the microturbulence, especially for coolest metal-rich stars.
This leads to a huge scatter and high fluorine abundances for supersolar
metallicity stars, not seen in the trends from the weaker lines for the same
stars. When estimating the final mean fluorine abundance trend versus
metallicity, we neglect the fluorine abundances from the four strongest lines
(R7, R9, R11 and R12) for all stars and use only those derived from R16, R18,
and R19 for the coolest metal-rich stars. We confirm the flat trend of [F/Fe]
found in other studies in the metallicity range of -1.0<[Fe/H]<0.0. We also
find a slight enhancement at supersolar metallicities (0<[Fe/H]<0.15) but we
cannot confirm the upward trend seen at [Fe/H]>0.25. We need more observations
of M giants at super solar metallicities with a spectrometer like IGRINS to
confirm if the metal-rich fluorine abundance upturn is real or not.
