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This paper presents a new approach to the design of canonical dual-mode cavity filters within representation theory. Instead of the folded canonical coupling matrix, which results from using the resonances of the empty cavities as a basis, a representation based on the resonances of the cavities with all perturbations present is used. The resulting coupling matrix takes the form of a cul-de-sac configuration. For canonical dual-mode filters with a symmetric response, it allows direct design of the entire structure, except of the input cavity that requires optimization. A sixth-order filter with two symmetrically located transmission zeros is presented to document the validity of the approach. A sixth-order filter with two transmission zeros above the passband is also presented.