We construct an approximated solution to the equation of energy spectrum balance for developed decaying homogeneous isotropic turbulence. This equation is closed within the framework of statistical model based on the principle of maximal randomness with using renormalization group and $\epsilon$-expansion. We calculate the energy spectra and transfer functions in the case where the wave numbers lye in the energy-containing and inertial regions. In this case, the Kolmogorov constant is equal to $C_{\mathrm K}=1.55$. It is shown that the one-dimensional longitudinal spectrum for the energy, calculated with no free fitting parameters and normalized in the von Karman–Hovart energy units, is in good agreement with experimental data for decaying turbulence.