Abstract: Abstract It is known that a unital simple C * -algebra A with tracial topological rank zero has real rank zero. We show in this note that, in general, there are unital C * -algebras with tracial topological rank zero that have real rank other than zero. Let 0 → J → E → A → 0 be a short exact sequence of C * -algebras. Suppose that J and A have tracial topological rank zero. It is known that E has tracial topological rank zero as a C * -algebra if and only if E is tracially quasidiagonal as an extension. We present an example of a tracially quasidiagonal extension which is not quasidiagonal.