In this paper, the notion of transversal clauses is introduced and subsequently a new algorithm for computing prime implicants is developed. Opposed to the common approach of computing prime implicants of a dnf, the proposed algorithm uses a cnf representation of a propositional formula. The same algorithm applied on a dnf representation yields the set of prime implicates of a formula. Besides its suitability for implementation in a parallel environment and as an incremental algorithm, it has been found to work faster in case, the number of prime implicants is large.