In the calculation of KL0→γγ to first order in SU(3) breaking, one must include not only η-η′ mixing but also the first-order corrections to the SU(3) relations for the K→η and η→γγ transitions. We calculate the leading corrections to these processes at one loop in chiral perturbation theory. Although not large in themselves, they can have potentially large effects in K→γγ due to the cancellations among the leading SU(3) invariant terms. We also comment on corresponding effects on the dispersive part of the KL− KS mass differences.