Global　Navigation　Satellite　System　(GNSS)-based　cooperative　positioning　is　highly　degraded　in　dense　urban　areas　due　to　non-line-of-sight　(NLOS)　and　multipath　effects.　Multiple　simultaneous　faulty　GNSS　measurements　can　result　in　traditional　fault　detection　and　exclusion　(FDE)　methods　finding　a　consistent　but　erroneous　group　of　satellites.　This　paper　describes　a　novel　distributed　FDE　method　based　on　cooperative　reliability　message　(CRM),　which　is　suitable　for　cooperative　positioning　system　in　connected　vehicles.　The　idea　is　to　take　into　account　not　only　the　consistency　check　on　raw　GNSS　measurements,　but　also　the　prior　knowledge　about　the　quality　of　GNSS　measurements　offered　by　nearby　cooperators　so　as　to　improve　the　ability　to　exclude　multiple　GNSS　faults.　The　line-of-sight　(LOS)　satellites　identified　by　cooperators　are　stored　in　CRMs,　which　will　be　shared　to　the　host　vehicle　to　generate　the　candidates　for　the　set　of　LOS　satellites　observed　locally.　Based　on　the　candidates,　a　bottom-up　searching　strategy　is　designed　to　find　the　healthy　satellites　and　isolate　the　faulty　ones　precisely.　Several　experiments　involving　four　moving　vehicles　were　conducted　in　dense　urban　areas.　Results　indicate　the　superiority　of　CRM-based　method　in　excluding　multiple　faults　over　existing　methods.