A framework is presented for including second-order perturbative corrections to the radiation patterns of parton showers. The formalism allows to combine O(alphaS^2)-corrected iterated 2->3 kernels for ordered gluon emissions with tree-level 2->4 kernels for unordered ones. The combined Sudakov evolution kernel is thus accurate to O(alphaS^2). As a first step towards a full-fledged implementation of these ideas, we develop an explicit implementation of 2->4 shower branchings in this letter.
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