  This note presents explicit matrix expressions of a class of
recently-discovered non-diagonal K-matrices for the trigonometric
$A^{(1)}_{n-1}$ vertex model. From these explicit expressions, it is easily
seen that in addition to a {\it discrete} (positive integer) parameter $l$,
$1\leq l\leq n$, the K-matrices contain $n+1$ (or $n$) continuous free boundary
parameters.
