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2 ) be the algebraic transfer, which is defined by W. Singer as an algebraic version of the geometrical transfer. It has been shown that the algebraic transfer is highly nontrivial and, more precisely, that T r k is an isomorphism for k = 1, 2, 3. However, Singer showed that T r 5 is not an epimorphism. In this paper, we prove that T r 4 does not detect the nonzero element gs ∈ Ext 4,12·2 s A (F 2 , F 2 ) for every s ≥ 1. As a consequence, the localized (Sq 0 ) −1 T r 4 given by inverting the squaring operation Sq 0 is not an epimorphism. This gives a negative answer to a prediction by Minami.

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