Proposition 3.1 of the paper Annihilators and the CS-condition, Glasgow Math. J. 40 (1998), 213–222, is incorrect as stated, and consequently the note added in proof is incorrect. Hence the question of Faith and Menal whether every strongly right Johns ring is quasi- Frobenius remains open. The problem is that the assumption that the left socle S1 and the right socle Sr are equal is not established. All we know is that Si⊆Sr = r(J) = l(J) by [8, Lemma 2.2]. We can prove the following result.