  We show that the exact integrator for the classical Kepler motion, recently
found by Kozlov ({\it J. Phys. A: Math. Theor.\} {\bf 40} (2007) 4529-4539),
can be derived in a simple natural way (using well known exact discretization
of the harmonic oscillator). We also turn attention on important earlier
references, where the exact discretization of the 4-dimensional isotropic
harmonic oscillator has been applied to the perturbed Kepler problem.
