We present chemical abundances in three red giants and two turn-off stars in the metal poor Galactic globular cluster (GC) NGC 6397 based on spectroscopy obtained with the MIKE high resolution spectrograph on the Magellan 6.5-m Clay telescope. Our results are based on a line-by-line differential abundance analysis relative to the well-studied red giant Arcturus and the Galactic halo field star Hip 66815. At a mean of -2.10 +/- 0.02 (stat.) +/- 0.07 (sys.) the differential iron abundance is in good agreement with other studies in the literature based on gf-values. As in previous, differential works we find a distinct departure from ionization equilibrium in that the abundances of Fe I and Fe II differ by ~0.1 dex, with opposite sign for the RGB and TO stars. The alpha-element ratios are enhanced to 0.4 (RGB) and 0.3 dex (TO), respectively, and we also confirm strong variations in the O, Na, and Al/Fe abundance ratios. Accordingly, the light-element abundance patterns in one of the red giants can be attributed to pollution by an early generation of massive SNe II. TO and RGB abundances are not significantly different, with the possible exception of Mg and Ti, which is, however, amplified by the patterns in one TO star, additionally belonging to this early generation of GC stars. We discuss interrelations of these light elements as a function of the GC metallicity.