Symmetry description of wavefunctions of Cooper pairs, based on the Pauli exclusion principle and on the Mackey-Bradley theorem, is carried out for the space groupsD2h1 andD4h17. The table of the irreducible representations of Cooper pairs in theL-S and thej-j coupling is presented. The nodal structure of the pairing function in the time-reversal symmetry violation is investigated. It is shown that if the time-reversal symmetry is violated in the strong spin-orbit coupling case, line nodes are possible for the odd superconducting order parameter.