Traditional algorithms for prime implicate generation [Quine, 1952; McCluskey, 1956; Tison, 1967; Kean and Tsiknis, 1990; de Kleer, 1992] require the input formulas to be first transformed into a CNF formula. This process, however, requires exponential time in the worst case and can result in an exponential blow up of the input size. Such cases occur frequently when the problem domains are best characterized by some DNF formulas. In this paper, we study a new algorithm which allows a more general input: a conjunction of DNF formulas. We wil l present empirical results comparing the new algorithm with some existing implementations, and discuss how it can be used in a propositional abductive reasoning system.