We show that, in the conventional chiral $\mathrm{SU}\left(2\right)\mathrm{}\otimes \mathrm{SU}\left(2\right)\mathrm{}$-symmetric nonlinear Lagrangian models of pseudoscalar mesons, scale invariance is essentially broken. Although a dilatation current ${\mathcal{D}}^{\mu }\mathrm{}\left(x\right)\mathrm{}$ generating a scale transformation for the meson fields can be explicitly constructed, it is impossible to choose a canonical frame in which the axial-vector current transforms with scaling dimension 3 under this scale transformation. The conflict between scale invariance and the nonlinear realization of chiral symmetry is exhibited through the chiral nonvariance of the new energy-momentum tensor ${\theta }^{\mu \nu }$, which gives ${\mathcal{D}}^{\mu }\mathrm{}\left(x\right)=x_{\nu }{\theta }^{\mu \nu }\mathrm{}\left(x\right)\mathrm{}$ and ${\partial }_{\mu }{\mathcal{D}}^{\mu }\mathrm{}\left(x\right)={{\theta }_{\mu }}^{\mu }\mathrm{}\left(x\right)\mathrm{}$. Furthermore, we also show that, in nonlinear models, there is no chiral-symmetric tensor which can approach this new energy-momentum tensor in the free-field limit.

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