The general two‐electron wavefunctions obeying the Pauli exclusion principle and Anderson criteria for Cooper pairs are constructed for D2hand D4hsymmetries. It is shown that in axial symmetry groups the Blount theorem is violated and lines of nodes of triplet superconducting order parameter are required by the symmetry. Application of the results to high −Tcsuperconductors is discussed. © 2003 American Institute of Physics