  A proof is given that the polar decomposition procedure for unitarity
restoration works for products of invertible nonunitary operators. A brief
discussion follows that the unitarity restoration procedure, applied to
propagators in spacetimes containing closed timelike curves, is analogous to
the original introduction by Feynman of ghosts to restore unitarity in
non-abelian gauge theories. (The substance of this paper will be a note added
in proof to the published version of gr-qc/9405058, to appear in Phys Rev D.)
