A joint particle imaging velocimetry/laser-induced OH fluorescence (PIV/OH-LIF) imaging technique was applied to measure the conditional unburned and burned gas velocities in turbulent premixed Bunsen flames of lean hydrogen/air mixtures. Turbulent scalar flux u "c " in a two-dimensional plane was obtained for five dames with u ' /S-L ranging from 1.2 to 3. Flow integral length scales were also derived from PIV measurements based on the two-point correlation functions of the axial velocity fluctuation. Among the investigated flames, counter-gradient diffusion was observed in the radial component, while gradient diffusion was found in the axial component of u "c ". The behavior of countergradient diffusion is consistent with predictions from the Bray number expression. It is, however, contrary to the expectation that turbulent premixed flames will behavior in a gradient-diffusion manner for fuel-air mixtures with conditional dilatation peaking near the unburned side in laminar flame fronts. For the statistically two-dimensional turbulent flow field of the jet flame configuration, the axial convective and turbulent di:diffusive fluxes of the progress variable variance parallel to the turbulent flame brush do not vanish after applying Gauss's theorem. This invalidates the unique relationship between turbulent scalar flux and conditional dilatation found by Swaminathan et al.