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A new formulation of the quantum integrability condition for spin systems is proposed. It eliminates the ambiguities inherent in formulations derived from a direct transcription of the classical integrability criterion. In the new formulation, quantum integrability of an N-spin system depends on the existence of a unitary transformation which expresses the Hamiltonian as a function of N action operators. All operators are understood to be algebraic expressions of the spin-components with no restriction to any nite-dimensional matrix representation. The consequences of quantum (non-)integrability on the structure of quantum invariants are discussed in comparison with the consequences of classical (non-)integrability on the corresponding classical invariants. Our results indicate that quantum integrability is universal for systems with N = 1 and contingent for systems with N ≥ 2.