  Magneto-transmission measurements in magnetic fields in the range B=20-60T
have been performed to probe the H and K-point Landau level transitions in
natural graphite. At the H-point, two series of transitions, whose energy
evolves as $\sqrt{B}$ are observed. A reduced Slonczewski, Weiss and McClure
(SWM) model with only two parameters to describe the intra-layer (gamma0) and
inter-layer (gamma1) coupling correctly describes all observed transitions.
Polarization resolved measurements confirm that the observed apparent splitting
of the H-point transitions at high magnetic field cannot be attributed to an
asymmetry of the Dirac cone.
