Denote by the mod 2 Steenrod algebra. We study the algebraic transfer  constructed by Singer [15]. It is one of the useful  tools for studying the cohomology of the Steenrod algebra, Based on the results of Tangora [18], Lin [9], Chen [4], Lê [8] and Singer [15], we conclude that the non-zero element  is in the image of  (see [12]). Here denotes the Adams element in  and  In this note, we give another direct proof of this result. More specifically, we prove this by direct computations using the representation in the -lambda algebra of

Adams spectral sequences, Steenrod algebra, algebraic transfer.