Is it possible to make $R = \{(1, 0), (0, 1) \}$ antisymmetric without removing elements?

Question

I was wondering if I have the relation $R = \{(1, 0), (0, 1) \}$, is there any way I can make the relation antisymmetric without removing elements? I think not, because since the first part of the anti-symmetric implication is true, there is no way the second part $a = b$ will ever be true as long as the initial two elements are part of the relation.