We introduce a binary operation on strings (blocks) of elements from the set {0,1,\dots, m-1}, where m is an arbitrary integer greater than 1. This operation is an extension of one introduced by Konrad Jacobs and Michael Keane in the 1960's for blocks of 0's and 1's. We show that the extended operation is associative, introduce the concept of similar, cyclic, and circular blocks and provide a unique factorization theorem under this operation up to the similarity of the factors. We also give the conditions for commutativity of indecomposable blocks.