This paper describes two methods which generate all the prime implicants (PI's) quickly by using the directions of adjacency tavle (DA-table) that gives the knowledge of adjacency relations among the given minterms. One is a graphical method that enables us to generate PI's by hand, the other is a checking method that determines the existance of PI's quickly when it is programmed on a digital computer. And a fast minimization algorithm will be shown in this paper that can be implemented with reduced computational effort by selecting essential prime implicants (EPI's) first of all and using the concept of the integration of the PI identification and selection procedure. The procedure, proposed in this paper, has all the advantage of Karnaugh mapping, so the procedure is simple and easy.