We have extended our previous applications of the method of unitary clothing transformations (UCTs) in mesodynamics [1, 2] to quantum electrodynamics (QED) [3, 4]. An analytical expression for the QED Hamiltonian in the clothed-particle representation (CPR) has been derived. Its distinctive feature is the appearance of a new family of the Hermitian and energy independent interaction operators built up in the e^2-order for the clothed electrons and positrons instead the primary canonical interaction between electromagnetic and electron-positron fields. The problem of describing the bound states in QED in case of the positronium system has been considered. The first correction to the energy of the ground state of the para-positronium and its decay rate to two photons has been calculated by using the new interaction operators.