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A series of direct numerical simulations of the fully developed plane Couette fl ow at a Reynolds number of 6000 (based on the relative wall speed and half the channel height h) with different streamwise and spanwise lengths are con-ducted to investigate the effects of the computational box sizes on the secondary fl ow (SF). Our focuses are the number of counter-rotating vortex pairs and its relationship to the statistics of the mean fl ow and the SF in the small and moderate computational box sizes. Our results show that the number of vortex pairs is sensitive to the computational box size, and so are the slope parameter, the rate of the turbulent kinetic energy contributed by the SF, and the ratio of the kinetic energy of the SF to the total kinetic energy. However, the averaged spanwise width of each counter-rotating vortex pair in the plane Couette fl ow is found, for the first time, within 4(1 ± 0.25)h despite the domain sizes.