Unitarity Restoration for the Product of Nonunitary Operators

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.)