The steady state flow of a concentrated dispersion of starlike micelles above the colloidal glass transition concentration is interrogated by superimposing a small amplitude straining motion orthogonal to the main flow direction. Strain amplitude sweeps reveal that the linear response region of the orthogonal perturbation increases with increasing flow rate, consistent with a fluidization of the materials. Orthogonal dynamic frequency sweeps (ODFSs) are obtained for a wide range of shear rates probing the full flow curve. The shear-induced fluidization of the initially glassy suspension is more clearly evidenced by the appearance of a crossover frequency omega(c) in ODFS, which steadily increases, reflecting a faster structural relaxation under shear. The dependence of omega(c) on the shear rate is sublinear and follows a power law with an exponent of 0.8. We show that the shape of the orthogonal viscoelastic spectrum changes at a critical shear rate <(gamma) over dot>(cr), indicative of a structural relaxation modulus that changes from exponential at lower shear rates to multistep with alternating exponential and power law response at higher shear rates. We finally provide a theoretical framework which explains the observed sublinear power law dependence of the crossover frequency and relates it with the shear rate dependence of the viscosity measured by the flow curve. (C) 2019 The Society of Rheology.