Non-diagonal solutions of the reflection equation for the trigonometric $A_{n-1}^{(1)}$ vertex model

We obtain a class of non-diagonal solutions of the reflection equation for the trigonometric $A_{n-1}^{(1)}$ 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 $l$, $1\le l\le n$, the solution contains $n+2$ {\it continuous} boundary parameters.