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We conducted three-dimensional numerical simulation of Taylor-Couette flow with MHD interaction in a rotating co-axial cylinder, which results in the herringbone-like high-speed streak structures emerging in the vicinity of the inner wall. This is due to the strong Lorenz force, which suppresses turbulence and produces a pair of steady Taylor vortex cells. A high-speed streak near the inner wall is induced by a local vortex pair. These pairs are generated in the vicinity of the upper and lower walls as well as in the center of the channel. The generated vortices are transported by the Taylor vortex cell and azimuthal flow. Therefore, we concluded that the chain of phenomena produces the herringbone-like high-speed streak structures.