A method for investigating the adiabatic potential of two-centre vibronic systems employing one-centre symmetrized nuclear coordinates is proposed. The local nuclear coordinates of different centres are interdependent because the centres have common atoms. The coupling equations for these coordinates are obtained for an arbitrary two-centre system having reflection symmetry sigma(h). The extrema of the adiabatic potential are investigated under the additional conditions imposed by these coupling equations. As an example of the above approach the general expression for the sheets of adiabatic potentials of bioctahedra is obtained and the simplest case of a top-shared bioctahedron is investigated.