In order to specify cosmologically motivated initial conditions for major galaxy mergers (mass ratios ≤ 4:1) that are supposed to explain the formation of elliptical galaxies we study the orbital parameters of major mergers of cold dark matter halos using a high-resolution cosmological simulation. Almost half of all encounters are nearly parabolic with eccentricities $e \approx 1$ and no correlations between the halo spin planes or the orbital planes. The pericentric argument ω shows no correlation with the other orbital parameters and is distributed randomly. In addition we find that 50% of typical pericenter distances are larger than half the halo's virial radii which is much larger than typically assumed in numerical simulations of galaxy mergers. In contrast to the usual assumption made in semi-analytic models of galaxy formation the circularities of major mergers are found to be not randomly distributed but to peak around a value of $\epsilon \approx 0.5$. Additionally all results are independent of the minimum progenitor mass and major merger definitions (i.e. mass ratios ≤ 4:1; 3:1; 2:1).