  We explain how to construct matrix product stationary states which are
composed of finite-dimensional matrices. Our construction explained in this
article was first presented in a part of [Hieida and Sasamoto:J. Phys. A: Math.
Gen. 37 (2004) 9873] for general models. In this article, we give more details
on the treatment than in the above-mentioned reference, for one-dimensional
asymmetric simple exclusion process(ASEP).
