  We study the automorphisms of the non-split Cartan modular curves $X_{ns}(p)$
of prime level $p$. We prove that if $p\geq 37$ all the automorphisms preserve
the cusps. Furthermore, if $p\equiv 1\text{ mod }12$ and $p\neq 13$, the
automorphism group is generated by the modular involution given by the
normalizer of a non-split Cartan subgroup of $\text{GL}_2(\mathbb F_p)$. We
also prove that for every $p\geq 37$ such that $X_{ns}(p)$ has a CM rational
point, the existence of an exceptional rational automorphism would give rise to
an exceptional rational point on the modular curve $X_{ns}^+(p)$ associated to
the normalizer of a non-split Cartan subgroup of $\text{GL}_2(\mathbb F_p)$.
