\textit{A. Beurling} [Lectures 4 and 5, AMS Summer Institute, Stanford (1961)] has used subadditive weight functions \(\omega\) to define non- quasianalytic classes of ultradifferentiable functions \({\mathcal E}_{(\omega)} (\mathbb{R})\). Some authors also have defined different weight functions for the classes \({\mathcal E}_{(\omega)} (\mathbb{R})\). \textit{R. W. Braun}, \textit{R. Meise} and \textit{B. A. Taylor} [Result. Math. 17, No. 3/4, 206-237 (1980; Zbl 0735.46022)] have shown that there exists a weight function \(\omega\) which cannot be dominated by subadditive weight functions \(\sigma\) in the sense of Beurling. In the present paper concrete examples of weight functions \(\omega\) with this property are given.