We have studied the dissociation of the trifluoromethane molecule, CHF3, into negative ionic fragments at the C 1s and F 1s edges. The measurements were performed by detecting coincidences between negative and positive ions. We observed five different negative ions: F-, H-, C-, CF-, and F-2(-). Their production was confirmed by the analysis of triple coincidence events (negative-ion/positive-ion/positive-ion or NIPIPI coincidences) that were recorded with cleaner signals than those of the negative-ion/positive-ion coincidences. The intensities of the most intense NIPIPI coincidence channels were recorded as a function of photon energy across the C 1s and F 1s excitations and ionization thresholds. We also observed dissociation channels involving the formation of one negative ion and three positive ions. Our results demonstrate that negative-ion/positive-ion coincidence spectroscopy is a very sensitive method to observe anions, which at inner-shell edges are up to three orders of magnitude less probable dissociation products than cations.