The process of scattering of coherent diffraction radiation (CDR) generated by short electron bunch on one of the subsequent bunches of the accelerator is considered. CDR spectrum from bunch passing through circular aperture in an ideally conducting disc have been calculated. It is shown that the CDR yield is suppressed significantly in the soft part of the spectrum due to finite outer radius of the disc. The use of the concave mirror with central hole instead of the flat disc with aperture is proposed. The focusing of the backward diffraction radiation onto following bunch may be possible in this case. The estimation of the yield of scattered hard photons has been obtained, that is proportional to Ne3, where Ne is the number of electron per bunch.