The behaviour of longitudinal and transverse structure functions in the far field of a turbulent round jet is investigated experimentally. Attention is focused on the scaling exponents of structure functions within the inertial range. Different initial conditions represented by different turbulent intensities at the jet nozzle are considered. The difference between the scaling exponents of longitudinal and transverse structure functions is found to be almost independent of the initial conditions. The majority of this difference depends on the anisotropy of the flow field and the difference also decreases with increasing Reynolds number.