  A tuple of commuting operators $(S_1,\dots,S_{n-1},P)$ for which the closed
symmetrized polydisc $\Gamma_n$ is a spectral set is called a
$\Gamma_n$-contraction. We show that every $\Gamma_n$-contraction admits a
decomposition into a $\Gamma_n$-unitary and a completely non-unitary
$\Gamma_n$-contraction. This decomposition is an analogue to the canonical
decomposition of a contraction into a unitary and a completely non-unitary
contraction. We also find new characterizations for the set $\Gamma_n$ and
$\Gamma_n$-contractions.
