A non-LTE analysis of K I resonance lines at 7664.91 and 7698.97 A was carried out for 15 red giants belonging to three globular clusters of different metallicity (M 4, M 13, and M 15) along with two reference early-K giants (rho Boo and alpha Boo), in order to check whether the K abundances are uniform within a cluster and to investigate the behavior of [K/Fe] ratio at the relevant metallicity range of -2.5 <[Fe/H] < -1. We confirmed that [K/H] (as well as [Fe/H]) is almost homogeneous within each cluster to a precision of < ~0.1 dex, though dubiously large deviations are exceptionally seen for two peculiar stars showing signs of considerably increased turbulence in the upper atmosphere. The resulting [K/Fe] ratios are mildly supersolar by a few tenths of dex for three clusters, tending to gradually increase from ~+0.1-0.2 at [Fe/H] ~-1 to ~+0.3 at [Fe/H] ~ -2.5. This result connects reasonably well with the [K/Fe] trend of disk stars (-1 < [Fe/H]) and that of extremely metal-poor stars (-4 <[Fe/H] < -2.5). That is, [K/Fe] appears to continue a gradual increase from [Fe/H]~0 toward a lower metallicity regime down to [Fe/H]~-3, where a broad maximum of [K/Fe]~+0.3-0.4 is attained, possibly followed by a slight downturn at [Fe/H]<~-3.
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