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 ω c in ODFS, which steadily increases, reflecting a faster structural relaxation under shear. The dependence of ω 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 γ 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. © 2019 The Society of Rheology.