It is demonstrated that the degenerate Coriolis splitting of a rotational level, $K\ne 0$, of a molecule which is in an excited perpendicular vibration state is influenced by centrifugal distortion. The effect is of the form $a{K}^3+bJ(J+1\mathrm{})K$. The effect of this distortion on the infra-red spectrum is of the same order of magnitude as the ordinary centrifugal distortion. It is further shown that by redefining the Coriolis coupling coefficient ${\zeta }_t$ the rotational energy of a symmetric molecule may be written in the form $\left(\frac{E}{\mathrm{hc}}\right)=\left[J\right(J+1\mathrm{})-K^2]B_v+L^2{C}_v-{\mathrm{}\left[J\right(J+1\mathrm{})-K^2]}^2{D}_J-\left[J\right(J+1\mathrm{})-K^2]L^2{D}_{\mathrm{JL}}-L^4{D}_L$ where $L=K-\Sigma t^{}{l}_t\zeta _t^{}{}_{}{}^{\mathrm{}\left(z\right)\mathrm{}}$.

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