  A general quantum electrodynamic method for derivation of nuclear recoil
corrections in hydrogenic systems, which are exact in the nuclear charge
parameter $Z\,\alpha$, is introduced. The exemplary derivation is presented for
the $O(m/M)$ nuclear pure recoil correction to the hyperfine splitting. The
obtained result is verified by comparison to the known $(Z\,\alpha)^5$
contribution
