The staff of the Institute of High-Energy Physics together with researchers from Russian and foreign scientific centers have discovered a new physical phenomenon – reflection of fast charge particles in curved crystals. This article presents the first experimental results using multiple reflections of protons in silicon crystals to increase the beam collimation efficiency in the U-70 accelerator. The experimental data are compared with theoretical models. The technology developed using reflecting crystals can be used to form oppositely propagating beams in accelerators and has prospects for extracting low-emittance beams on ~1 GeV accelerators for electronuclear facilities and in medicine and industry.