Variation in the dynamics of a steady-state blood flow through a stenosed tapered artery has been investigated corresponding to changes in thixotropic parameter, $\lambda$ over the range [0,1]. To probe the role of parameter, $\lambda$ and differentiate the current model from other known non-Newtonian models, expressions of axial velocity, shear stress, wall shear stress and flow rate have be calculated depending upon this parameter and pressure gradient. Also, pressure gradient has been deduced uniquely with the help of continuity equation. Our choice of calculating pressure gradient has led to obtaining shear stress such that its dependence on structural parameter of our model, unlike most of available results, motivates for further investigation. The simultaneous effects of varying yield stress and parameter, $\lambda$ on axial velocity, flow resistance and flow rate have been studied such that the differences between Herschel-Bulkley fluid model and our current model can be pointed out. To validate the suitability of our model and some results in history, we have also obtained limiting results for particular values of $\lambda$.