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It is shown that for each mixed state there exists a Schmidt (super statevector) decomposition in terms of Hermitian operators. Its utilization forfinding all twins is illustrated in full detail in the case of the twospin-one-half-particle states with maximally disordered subsystems (mixtures ofBell states).Comment: 22 pages, Latex2e, supersedes both quant-ph/0106101 and  quant-ph/010603

Hermitian Schmidt decomposition and twin observables of bipartite mixed states