Abstract. Let p(n) denote the ordinary partition function. Subbarao conjectured that in every arithmetic progression r (mod t) there are infinitely many integers N r (mod t) for which p(N) is even, and infinitely many integers M r (mod t) for which p(M) is odd. In the even case the conjecture was settled by Ken Ono. We prove the odd part of the conjecture which together with Ono's result implies the full conjecture.