[en] The aim of the paper is to prove the gauge invariance of the Coulomb Hamiltonian, which is obtained through the exclusion of the longitudinal and scalar components of the vector-potential. The exclusion is produced with the help of classical equations of motion, which follow from the initial Lagrangian. The proof of the resulting Hamiltonian gauge-invariance removes based on gauge invariance objections againts the preceeding work, where the condition, which determines the admissible values of the nonrenormalized charge in quantum electrodynamics has been stated