(KSKS0)-K-0 production in two-photon collisions has been studied using a 397.6 fb(-1) data sample collected with the Belle detector at the KEKB e(+)e(-) collider. For the first time the cross sections are measured in the two-photon center-of-mass energy range between 2.4 GeV and 4.0 GeV and angular range vertical bar cos theta*vertical bar < 0.6. Combining the results with measurements of gamma gamma -> K+K- from Belle, we observe that the cross section ratio sigma((KSKS0)-K-0)/sigma(K+K-) decreases from similar to 0.13 to similar to 0.01 with increasing energy. Signals for the chi(c0) and chi(c2) charmonium states are also observed. (C) 2007 Elsevier B.V. All rights reserved.