  Given a CNF formula $F$, we present a new algorithm for deciding the
satisfiability (SAT) of $F$ and computing all solutions of assignments. The
algorithm is based on the concept of \emph{cofactors} known in the literature.
This paper is a fallout of the previous work by authors on Boolean
satisfiability \cite{sul1, sul2,sude}, however the algorithm is essentially
independent of the orthogonal expansion concept over which previous papers were
based. The algorithm selects a single concrete cofactor recursively by
projecting the search space to the set which satisfies a CNF in the formula.
This cofactor is called \emph{projective cofactor}. The advantage of such a
computation is that it recursively decomposes the satisfiability problem into
independent sub-problems at every selection of a projective cofactor. This
leads to a parallel algorithm for deciding satisfiability and computing all
solutions of a satisfiable formula.
