The An−1(1) trigonometric vertex model with {\it generic
non-diagonal} boundaries is studied. The double-row transfer matrix of the
model is diagonalized by algebraic Bethe ansatz method in terms of the
intertwiner and the corresponding face-vertex relation. The eigenvalues and the
corresponding Bethe ansatz equations are obtained.Comment: Latex file, 25 pages; V2: minor typos corrected, the version appears
in JHE