Author’s summary: In a 1991 paper, Asher Peres and the author theoretically analyzed a set of unentangled bipartite quantum states that could apparently be distinguished better by a global measurement than by any sequence of local measurements on the individual subsystems. The present paper returns to the same example, and shows that the best result so far achieved can alternatively be attained by a measurement that, while still global, is “unentangled” in the sense that the operator associated with each measurement outcome is a tensor product.