Relatively good quality isotropy is observed in the central region of a turbulent boundary layer developing over a mesh screen rough wall. Spectra of velocity and, more especially, vorticity fluctuations satisfy isotropy over a significant wavenumber range. Inertial range scaling exponents ζu2(p) and ζu3(p) of moments of order p(?8) of increments of the transverse velocity fluctuations u2 and u3 are significantly smaller than the exponents ζu1(p) of increments of the longitudinal velocity fluctuation u1. Exponents inferred from the locally averaged values of squared transverse vorticity fluctuations are only slightly smaller than ζu1(p). The difference between ζu1(p) and ζu2(p) [or ζu3(p)] more likely reflects the departure from isotropy of inertial range scales. There is evidence to suggest that the difference decreases with an increase in the Reynolds number and/or a decrease in the magnitude of the mean shear.