The 56Fe international covariance matrices recommend variances for capture, elastic, and inelastic cross sections. Analysis shows that these matrices are often inconsistent and unrealistic. A new covariance matrix was established on the basis of feedback from the interpretation of two integral benchmarks representative of Generation III and Generation IV reflectors. Flux attenuation in the reflector at various energies demonstrates good agreement between calculation and experiment. The RDN code based on a nonlinear regression method using an iterative technique (limited to the first Gauss-Newton iteration in this study) was used to reestimate 56Fe cross sections and to deduce the a posteriori covariance matrix associated with the JEFF3.1.1 library. The results highlight that the 56Fe cross-section levels in the JEFF3.1.1 library are satisfactory. The new covariance matrix can then be used as a reference to calculate uncertainty propagation.