Complementary sequence sets (CSSs) and complete complementary codes (CCCs) have many applications in science and engineering, especially in wireless communications. A construction of CSS and CCC, having size M = 2^m and length M^K, where m and K are positive integers, is presented. The proposed construction is a generalized paraunitary (PU) algorithm that greatly increases the number of permutations from K! to (mK)! compared to those of previous PU constructions. Moreover, this new construction can be generalized to the case M = p^m, where p is a positive integer. The increase in the number of permutations means that a wide range of CCCs and CSSs can be obtained.