We investigate the problem of decomposing a language into a catenation of nontrivial languages, none of which can be decomposed further. In many cases this leads to the operation of an ordered catenation closure, introduced in this paper. We study properties of this operation, as well as its iterations. Special emphasis is on laid on ordered catenation closures of finite languages. It is also shown that if an infinite language is a code or a length code, then its ordered catenation closure does not possess a finite decomposition of indecomposable factors.