Multinucleon transfer mechanism in the collision of U-238 + U-238 system is investigated at E-c.m. = 833 MeV in the framework of the quantal diffusion description based on the stochastic mean-field approach. Double cross sections sigma (N, Z) as a function of the neutron and proton numbers, the cross sections sigma(Z) and sigma(A) as a function of the atomic numbers and the mass numbers are calculated for production of the primary fragments. The calculation indicates the U-238 + U-238 system may be located at an unstable equilibrium state at the potential energy surface with a slightly negative curvature along the beta stability line on the (N, Z) plane. This behavior may lead to rather large diffusion along the beta stability direction.