  For a positive integer $k$, we say that an association scheme $(\Omega,S)$ is
$k$-equivalenced if each non-diagonal element of $S$ has valency $k$.
$k$-equivalenced is weaker than pseudocyclic. It is known that every
$k$-equivalenced association scheme is Frobenius when $k=2,3$ and every
$4$-equivalenced association scheme is pseudocyclic. In this paper, we will
show that every $4$-equivalenced association scheme is Frobenius.
