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A full three-band model for the CuO$_{2}$ plane with inclusion of allessential interactions - Cu-O and O-O hopping, repulsion at the copper andoxygen and between them - is considered. A general procedure of the low-energyreduction of the primary Hamiltonian to the Hamiltonian of the generalized$t$-$t'$-$J$ model is developed. An important role of the direct O-O hopping isdiscussed. Parameters of the effective low-energy model (the hopping integral,the band position and the superexchange constant $J$ are calculated. Ananalysis of the obtained data shows that the experimental value of $J$ fixesthe charge transfer energy $\Delta =(\epsilon_{p}-\epsilon_{d})$ in a narrowregion of energies.Comment: 32 pp. (LATEX), two figures (PostScript) appende

Consistent low-energy reduction of the three-band model for copper oxides with O-O hopping to the effectivet-Jmodel