In this paper, we consider the partition function Q(n) counting the partitions of n into distinct parts and investigate congruence identities of the form
Q\left( {p \cdot n + {{{p^2} - 1} \over {24}}} \right) \equiv 0\,\,\,\left( {\bmod 4} \right),
where p ⩾ 5 is a prime.