The basic principles of an algorithm for the folding of programmable logic arrays (PLAs) are presented in this paper. The algorithm is valid for both column and row folding, although it has been described considering only the simple column folding. The pairwise compatibility relations among all the pairs of the columns of the PLA are mapped into a square matrix, called the compatibility matrix of the PLA. A foldable compatibility matrix (FCM), is then derived from the compatibility matrix. The algorithm presented in this paper is based on the FCM concept and the folding theorem, which states that the existence of an n x m FCM is both necessary and sufficient to fold 2m columns of an M-column PLA (2m ≤ n). Once an FCM is obtained, the ordered pairs of foldable columns and the reordering of the rows are readily determined. It has been conjectured that the algorithm produces the maximum folding of the PLA in all cases.