  We obtain a class of non-diagonal solutions of the reflection equation for
the trigonometric $A^{(1)}_{n-1}$ vertex model. The solutions can be expressed
in terms of intertwinner matrix and its inverse, which intertwine two
trigonometric R-matrices. In addition to a {\it discrete} (positive integer)
parameter $l$, $1\leq l\leq n$, the solution contains $n+2$ {\it continuous}
boundary parameters.
