I am confused about generating symmetry-adapted orbitals?

Question

Please refer to this link about generating the symmetry-adapted orbitals for ethylene:
http://chemistry.umeche.maine.edu/CHY556/Salcs2.html
They claim only two symmetry-adapted orbitals are possible from the combination of the carbon 2s and the hydrogen 1s orbitals. From the (S,S) carbons they add the (S,S) hydrogens to generate the sigma orbital that is bonding between C-C and bonding between C-H. From the (A,S) carbons they add the (A,S) hydrogens to get the sigma star orbital that is antibodning between C-C and antibonding between C-H. My question is that you should be able to generate two more orbitals. Why can't you subtract the (S,S) hydrogens from the (S,S) carbon to generate an orbital that is bonding between carbon and antibonding between hydrogen. Likewise, why can't you subtract the (A,S) hydrogens from the (A,S) carbons to generate an orbital that is antibonding between carbon but bonding between the hydrogens?

Answer 1

Yes you can ! They are what are called the anti bonding orbitals.