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We deal with the recent progress in the fabrication of the graded Co/C multilayer mirrors to be used in a 21x Schwarzschild objective (SO) operating at the wavelengths near 4.5 nm ("carbon window" region). The peak reflectivity of flat Co/C mirrors was measured to be 14.8% (wavelength of 4.48 nm, incidence angle of 5 degrees). The reflectivity curves of the spherical mirrors achieved 3%-6%, with the spectral matching accuracy being Deltad approximately 0.008 nm (Deltad/d approximately 0.3%). As a result the SO demonstrates a full working aperture (N(A) approximately 0.2) operation with the total throughput of 0.25%.