We present the results of a combined fit of the reactor antineutrino rates and the Daya Bay measurement of σ f,235 and σ f,239 . The combined fit leads to a better determination of the two cross sections per fission: σ f,235 = 6.29 ± 0.08 and σ f,239 = 4.24 ± 0.21 in units of 10 −43 cm 2 /fission, with respective uncertainties of about 1.2% and 4.9%. Since the respective deviations from the theoretical cross sections per fission are 2.5σ and 0.7σ, we conclude that, if the reactor antineutrino anomaly is not due to active-sterile neutrino oscillations, it is likely that it can be solved with a revaluation of the 235 U reactor antineutrino flux. However, the 238 U, 239 Pu, and 241 Pu fluxes, which have larger uncertainties, could also be significantly different from the theoretical predictions.The flux of electron antineutrinos produced in nuclear reactors is generated by the β decays of the fission products of 235 U, 238 U, 239 Pu, and 241 Pu. The 2011 recalculation [1, 2] of the four fluxes led to the discovery of the reactor antineutrino anomaly [3], which is a deficit of the rate of electron antineutrinos measured in several reactor neutrino experiments. There are two known possible explanations of the reactor antineutrino anomaly: 1) a miscalculation of one or more of the four electron antineutrino fluxes [4,5] and 2) active-sterile neutrino oscillations (see Ref.[6] and references therein). In this paper we consider the first possibility and we present an improvement of the results presented in Refs. [4,5] The cross section per fission σ f,235 of the 235 U electron antineutrino flux was determined in Ref.[4] with a fit of the reactor rates by taking into account the different fuel compositions. Recently the Daya Bay Collaboration presented a determination of σ f,235 and σ f,239 obtained by measuring the correlations between the reactor core fuel evolution and the changes in the reactor antineutrino flux and energy spectrum [5]. In this paper we present a combined fit of the reactor rates and the Daya Bay measurement of σ f,235 and σ f,239 which leads to a better determination of both cross sections per fission.In the analysis of the reactor rates, we consider the theoretical ratios [4]where f a k is the antineutrino flux fraction from the fission of the isotope with atomic mass k and the coefficient r k is the corresponding correction of the theoretical cross section per fission σ SH f,k which is needed to fit the data (k = 235, 238, 239, 241, denotes, respectively We analyze the data of the reactor rates with the leastsquares statisticwhere R exp a are the measured reactor rates listed in Table 1 of Ref. [6] and V R is the covariance matrix constructed with the corresponding uncertainties. The second term in Eq. (2) serves to keep under control the variation of the rates of the minor fissionable isotopes 238 U and 241 Pu, which are not well determined by the fit [4]. We consider ∆r 238 = 15% and ∆r 241 = 10%, which are significantly larger than the nominal theoretical uncertainties (respectively, 8.15% and...