  The "recoil" correction of order $m \alpha^6$ to the hyperfine splitting of
positronium ground state was found. The formalism employed is based on the
noncovariant perturbation theory in QED. Equation for two-particle component of
full (many-body) wave function is used, in which effective Hamiltonian depends
on the energy of a system. The effective Hamiltonian is not restricted to the
nonrelativistic region, so there is no need in any regularization. To evaluate
integrals over loop momenta, they are divided into "hard" and "soft" parts,
coming from large and small momenta respectively. Soft contributions were found
analytically, and hard ones are evaluated by numerical integration. Some soft
terms due to the retardation cancel each other. To calculate the "hard"
contributions, a great number of noncovariant graphs is replaced by only a few
covariant ones. The hard contribution was found in two ways. The first way is
to evaluate contributions of separate graphs, using the Coulomb gauge. The
second one is to calculate full hard contribution as a whole using the Feynman
gauge. The final result for the "recoil" correction is $0.381(6) m\al^6$ and
agrees with those of previous papers. Diagram-to-diagram comparison with the
revised results of Adkins&Sapirstein was done. All the results agree, so the
"recoil" correction is now firmly established. This means a considerable
disagreement with the experimental data.
