  Quantum channels can be mathematically represented as completely positive
trace-preserving maps that act on a density matrix. A general quantum channel
can be written as a convex sum of `extremal' channels. We show that for an
$N$-level system, the extremal channel can be characterized in terms of
$N^2$-$N$ real parameters coupled with rotations. We give a representation for
$N$= 2, 3, 4.
