  A necessary and sufficient condition in order that a (diagonalizable)
pseudohermitian operator admits an antilinear symmetry T such that T^{2}=-1 is
proven. This result can be used as a quick test on the T-invariance properties
of pseudohermitian Hamiltonians, and such test is indeed applied, as an
example, to the Mashhoon-Papini Hamiltonian.
