The intensity of Galactic cosmic rays is nearly isotropic because of the influence of magnetic fields in the Milky Way. Here, we present two-dimensional high-precision anisotropy measurement for energies from a few to several hundred teraelectronvolts (TeV), using the large data sample of the Tibet Air Shower Arrays. Besides revealing finer details of the known anisotropies, a new component of Galactic cosmic ray anisotropy in sidereal time is uncovered around the Cygnus region direction. For cosmic-ray energies up to a few hundred TeV, all components of anisotropies fade away, showing a corotation of Galactic cosmic rays with the local Galactic magnetic environment. These results have broad implications for a comprehensive understanding of cosmic rays, supernovae, magnetic fields, and heliospheric and Galactic dynamic environments.