  For any finite dimensional C^*-algebra A with a trace vector \vec s whose
entries are rational numbers, we give an endomorphism \Phi of the hyperfinite
II_1 factor R such that: for all k \in \mathbb {N}, \Phi^k (R)' \cap R=
\otimes^k A. The canonical trace \tau on R extends the trace vector \vec s on
A. Therefore the minimal projection is not necessarily equivalent to each
other.
