  New antineutrino spectra of fissile isotopes ($^{235}$U, $^{238}$U,
$^{239}$Pu and $^{241}$Pu) which are containing in a nuclear reactor fuel have
been obtained. A combined technique was used: calculation of antineutrino
spectra and their fitting to those obtained in the experiment at the Rovno NPP
in the 80s of the last century. The cross sections of fissile isotopes
calculated with these spectra describe well the cross section obtained
experimentally in the Double Chooz experiment. The calculated cross section for
the same reactor core composition is $\sigma_{f} = (5.82 \pm
0.12)\times10^{-43}$ cm$^2$/fission. It is the closest result between all
predicted. The obtained spectra have the same "bump" as experimental ones in 5
MeV observed energy region.
