  The matrix elements of relativistic nucleon-nucleon $(NN)$ potentials are
calculated directly from the nonrelativistic potentials as a function of
relative $NN$ momentum vectors, without using a partial wave decomposition. To
this aim, the quadratic operator relation between the relativistic and
nonrelativistic $NN$ potentials is formulated in momentum-helicity basis
states. It leads to a single integral equation for the two-nucleon $(2N)$
spin-singlet state and four coupled integral equations for two-nucleon
spin-triplet states, which are solved by an iterative method. Our numerical
analysis indicates that the relativistic $NN$ potential obtained using CD-Bonn
potential reproduces the deuteron binding energy and neutron-proton elastic
scattering differential and total cross-sections with high accuracy.
