We investigate a version of the periodic Anderson model in which both the d-and f-electron subsystems are strongly correlated. The one-site hybridization of the electron quantum states in each subsystem and the possibility of the d-electron hopping between lattice sites are taken into account. To construct the canonical transformation S-matrix, we use the system of one-site orthonormalized functions belonging to the zero Hamiltonian matrix of rank 16. We solve the problem exactly and determine the thermodynamic properties of the system in the approximation where the width of the conductance band vanishes. We use the diagram technique to investigate the delocalization of electrons in each subsystem and the renormalization of the one-particle Green's functions. We find the quasiparticle energy spectrum of delocalized electrons in the chain diagram approximation. We show that there are eight energy subbands in the symmetrical case.