  The eigenvalues of the Hamming graph $H(n,q)$ are known to be
$\lambda_i(n,q)=(q-1)n-qi$, $0\leq i \leq n$. The characterization of equitable
2-partitions of the Hamming graphs $H(n,q)$ with eigenvalue $\lambda_{1}(n,q)$
was obtained by Meyerowitz in [15]. We study the equitable 2-partitions of
$H(n,q)$ with eigenvalue $\lambda_{2}(n,q)$. We show that these partitions are
reduced to equitable 2-partitions of $H(3,q)$ with eigenvalue
$\lambda_{2}(3,q)$ with exception of two constructions.
