Particle diffusion transverse to a strong uniform magnetic field is studied within a three‐dimensional electrostatic guiding‐center model in which particle streaming along the magnetic field lines is admitted as well as transverseE×Bdrifting. Only the randomizing influence of thermal fluctuations excited by particle discreteness is considered. The electric field autocorrelation coefficient is obtained in the form of a modified fluctuation‐dissipation theorem. It is shown that because of the competition between the parallel and perpendicular decorrelation mechanisms, the divergence of the diffusion coefficient in the previous finite‐volume theories disappears. The diffusion coefficient is Bohm like (proportional to 1/B) for magnetic fields which are not too strong, and goes over to a classical variation (proportional to 1/B2) in the limitB→∞.