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The symmetrized polydisc of dimension three is the set Gamma(3) = {(z(1) + z(2) + z(3), z(1)z(2) + z(2)z(3) + z(3)z(1), z(1)z(2)z(3)) : |zi| <= 1, i = 1,2,3} subset of C-3. A triple of commuting operators for which Gamma(3) is a spectral set is called a Gamma(3)-contraction. We show that every Gamma(3)-contraction admits a decomposition into a Gamma(3)-unitary and a completely non-unitary Gamma(3)-contraction. This decomposition parallels the canonical decomposition of a contraction into a unitary and a completely non-unitary contraction. We also find new characterizations for the set Gamma(3) and Gamma(3)-contractions

On decomposition of operators having Γ_3 as a spectral set