  Exact integrability and algebraic Bethe ansatz of the small-polaron model
with the open boundary condition are discussed in the framework of the quantum
inverse scattering method (QISM). We employ a new approach where the fermionic
R-operator which consists of fermion operators is a key object. It satisfies
the Yang-Baxter equation and the reflection equation with its corresponding
K-operator. Two kinds of 'super-transposition' for the fermion operators are
defined and the dual reflection equation is obtained. These equations prove the
integrability and the Bethe ansatz equation which agrees with the one obtained
from the graded Yang-Baxter equation and the graded reflection equations.
