  Let $P$ be a preordered set, $R$ a ring and $FI(P,R)$ the finitary incidence
ring of $P$ over $R$. We find a criterion for all Jordan derivations of
$FI(P,R)$ to be derivations and generalize Theorem 3.3 from arXiv:1411.6123. In
particular, we prove that each Jordan derivation of the ring $RFM_I(R)$ of
row-finite $I\times I$-matrices over $R$ is a derivation, if $|I|>1$.
