In this paper we assume that all the carbon atoms in polyacetylene lie in the ground state under conditions of the tight-binding approximation (TBA) and choose the 2Pz orbital of hydrogen-like atoms as the ground-state wavefunction of an isolated carbon atoms. A linear combination of these orbitals is used as the π-electron wavefunction of polyacetylene. On the basis of this the multicenter integral problem is studied and then the analytic solution of the transfer integral for πelectrons is obtained.