The case k = a of the 1974 conjecture of Andrews on two partition functions A λ , k , a ( n ) and B λ , k , a ( n ) was proved by the first author and Sudha (1993) and the case k = a + 1 was established by the authors (2000). In this paper, we prove that the conjecture is false and give a revised conjecture for a particular case when λ is even.