  We rigorously prove that an extended Hubbard model with attraction in two
dimensions has an unconventional pairing ground state for any electron filling.
The anisotropic spin-0 or anisotropic spin-1 pairing symmetry is realized,
depending on a phase parameter characterizing the type of local attractive
interactions. In both cases the ground state is unique. It is also shown that
in a special case, where there are no electron hopping terms, the ground state
has Ising-type N\'eel order at half-filling, when on-site repulsion is
furthermore added. Physical applications are mentioned.
