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In this note, we consider M-curves of odd degree with real scheme of the form$< \mathcal{J} \amalg \alpha \amalg 1 < \beta > >$. With help of complexorientations, we prove that for $m = 9$, $\alpha \geq 2$, and for $m = 11$,$\alpha \geq 3$.

M-curves of degree 9 or 11 with one unique non-empty oval