  In this paper using one of the necessary conditions obtained for
extendability in [BISSar], we prove that the CAR flows ([Amo01]) on type III
factors arising from most quasi-free states are not extendable. As a
consequence we find the super product system of CAR flows. We know from [Arv03]
that CCR flows and CAR flows on type I factors with the same Arveson index are
cocycle conjugate. But our result together with [BISSar] will show that CCR
flows and CAR flows on type III factors are not cocycle conjugate.
