A multistage collimation system for the absorption of the growing halo of circulating beams is used at the Large Hadron Collider (LHC) to protect superconducting magnets and to ensure their reliable operation. A similar system is also planned for the Future Circular Collider (FCC). Studies for the improvement of the collimation system are performed prior to the operation of the LHC with a high luminosity. Studies have shown that one of the solutions to improve the beam collimation is the use of channeling in a short bent crystal, which serves as a primary collimator throwing particles deep into the secondary collimator by means of channeling. This system is very sensitive to the angular position of the crystal and various possible vibrations. In this work, another approach to beam collimation based on the bulk reflection of particles from bent crystal-lographic planes in a sequence of crystals has been proposed. Advantages of this scheme have been justified and a multistrip crystal device has been proposed to implement this scheme.