  Reflectionless CMV matrices are studied using scattering theory. By changing
a single Verblunsky coefficient a full-line CMV matrix can be decoupled and
written as the sum of two half-line operators. Explicit formulas for the
scattering matrix associated to the coupled and decoupled operators are
derived. In particular, it is shown that a CMV matrix is reflectionless iff the
scattering matrix is off-diagonal which in turn provides a short proof of an
important result of [Breuer-Ryckman-Simon]. These developments parallel those
recently obtained for Jacobi matrices.
