Two main features of the classical elementary divisor theory are the reduction of a matrix with integral coefficients to a normal form, which is a diagonal form with certain properties, and the uniqueness of such a normal form. The former of these two was extended to noncommutative domains by B. L. van der Waerdenf and J. H. M. Wedderburn,$ and a further contribution in this line was made by N. Jacobson.§ Moreover, O. Teichmuller|| showed recently that the so-called euclidean division process is unnecessary for the purpose and the weaker assumption that the domain is a principal ideal domain is sufficient. As for the second problem, namely the uniqueness problem, as it seems to me, little has been done in the noncommutative case except to show that the directly indecomposable components of the diagonal elements as a whole are, in virtue of the Krull-Remak-Schmidt theorem, unique up to similarity. In the present short note If we shall, generalizing a result in a joint note of K. Asano and the author,** see that the diagonal elements of a Jacobson-Teichmuller normal form themselves are determined uniquely up to similarity, although this uniqueness theorem is not so satisfactory and is essentially not so far from the uniqueness of the indecomposable components. Let / be a (not necessarily commutative) domain of integrity f t m