In this Letter, we introduce a new variant of the completely renormalized equation-of-motion method with singles, doubles, and non-iterative triples (CR-EOMCCSD(T)) that employs a novel strategy of handling the cluster product terms that naturally appears in the EOMCC-type expansion for the trial wavefunction. The new parametrization, as shown on several examples, including the N-2, C-2, and the ozone molecule, assures the required flexibility of the CR-EOMCCSD(T) approach especially in dealing with the challenging excited states primarily dominated by double excitations. (c) 2005 Elsevier B.V. All rights reserved.