Some semigroups without order are decomposable into t-archimedean semigroups via bands. In this paper, we deal with the decomposition of some ordered semigroups into t-archimedean components. The semilattice congruences play an important role in studying the decomposition of semigroups without order. When we pass from semigroups without order to ordered semigroups, the same role is played by the complete semilattice congruences. The characterization of complete semilattices of ordered semigroups of a given type has been considered by the same authors. The r-and l-band congruences have been proved to be useful in studying the decomposition of some types of ordered semigroups, especially the decomposition of r-and l-archimedean ordered semigroups. Band congruences have been proved to be useful in studying the decomposition of some types of ordered semigroups into t-archimedean (ordered) semigroups. The characterization of the bands of ordered semigroups of a given type T has been recently considered by the same authors. In this paper, we characterize the bands of t-archimedean ordered semigroups. As a result we get a decomposition of some ordered semigroups into t-archimedean components. The decomposition we obtain is uniquely defined.