Using the Dirac-Brueckner-Hartree-Fock ( DBHF ) approach including the hyperon degrees of freedom , we investigate the properties of neutron-star matter . To handle the hyperons in matter , we first examine the importance of the space part of baryon self-energies at high densities , and secondly study the effect of negative-energy states of baryons , which can provide an unambiguous relationship between the in-medium reaction matrices for baryon-baryon scattering and the baryon self-energies . We solve the coupled , Bethe-Salpeter equations in the nuclear-matter rest frame by using the Bonn potentials . We assume that eight kinds of nonstrange and strange mesons ( \sigma, \delta, \omega, \rho, \eta, \pi, K, K ^ { \ast } ) take part in the interactions between two baryons . Then , we calculate the baryon self-energies , the energy density and pressure of matter . The present calculation provides a hard equation of state in neutron-star matter at high densities , which is generated by the effect of Pauli exclusion , the short-range correlations between two baryons , etc . We finally predict the maximum neutron-star mass of 2.02 M _ { \odot } , which is consistent with both the recently observed masses , 1.97 \pm 0.04 M _ { \odot } ( J1614-2230 ) and 2.01 \pm 0.04 M _ { \odot } ( J0348+0432 ) .