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Let $C$ be a general canonical curve of genus $g$ defined over analgebraically closed field of arbitrary characteristic. We prove that if $g\notin \{4,6\}$, then the normal bundle of $C$ is semistable. In particular, if$g \equiv 1$ or $3$ mod $6$, then the normal bundle is stable.

The normal bundle of a general canonical curve of genus at least 7 is semistable