We propose a new optical arrangement of the double grating monochromator (DGRM), intended for use in a pure rotational Raman-lidar. The main idea of the construction proposed is in the use of optical monofibers, to couple two chambers of the DGRM. The coupling with optical monofibers enables isolation of two pairs of spectral portions in the S and O branches of the pure rotational Raman spectra (PRRS) of nitrogen and oxygen symmetric relative to the line of exciting radiation. The use of monofibers provides for optically summing the symmetric portions of the PRRS at the exit of the second monochromator, thus increasing the power of PRRS collected for further temperature retrieval. It is important that this approach provides for better than 107 suppression of the spectral line, due to unshifted Mie+Rayleigh scattering. As calculations and laboratory experiments show the end-to-end transmission of the DGRM, with the account of optical summing mentioned, can compare with the transmission of the interference filters available. At the same time, the DGRM provides better spectral purity of the RRS portions isolated, which is a crucial point of the Raman-lidar temperature measurements. Temperature profiles of the atmosphere acquired with the combined Raman- lidar of the Institute for Tropospheric Research in Leipzig, Germany, equipped with the DGRM proposed, showed a good agreement with the profiles measured with a radiosonge.