In order to study the mechanisms of the turbulent frictional drag reduction by surfactant additives, the drag reduction, the shear viscosity and the shear stress relaxation were measured for solutions of a cationic surfactant cetyltrimethyl ammonium bromide (CTAB) with the same molar sodium salicylate as a counter-ion. It is found that the first step relaxation time decreases with increasing concentration and, thus, with the maximum drag-reducing rates, which indicates that the stiffness of the micellar structures with the first relaxation time, increases with the increase of the concentration of CTAB. Furthermore, for this surfactant, a viscoelastic property is necessary for reducing drag, while a stronger viscoelasticity characterized by a tail relaxation time does not necessarily mean a higher drag-reducing rate.