Self-maps of modules over the Steenrod algebra John H. Palmieri Journal of Pure and Applied Algebra 79 (1992), 281-291. Abstract For a finite module M over the Steenrod algebra A, we prove the existence of a non-nilpotent element in Ext^{s;t}_A(M;M) "parallel to the vanishing line." We use this result to give a proof of Margolis' construction to kill Pts-homology groups, at all primes.