A bounded linear operator T on the Hilbert space H is called strongly irreducible if T does not commute with any nontrivial idempotentoperator. One says that T has a finite (SI) decomposition if T can be writtenas the direct sum of finitely many strongly irreducible operators. In this paper, we use the Ko-group of the commutant of operators to characterize operators with unique finite (SI) decomposition up to similarity. Also weshow that the Ko-group of H∞(Ω) is isomorphic to the integers, where is simply connected.