  We give a classification of the matrices in the unitary group U(1,1;H),where
H is the division ring of the real quaternions. To this end, we consider the
complex representation phi(P) for P in U(1,1;H). Next, we compute the
characteristic polynomial f of the 4x4 complex matrix phi(P) and then study the
sign of the resultant of f and its derivative f'.
