  Take a smooth, connected and non-degenerate projective curve $X\subset
\mathbb {P}^r$, $r\ge 2b+2\ge 6$, defined over an algebraically closed field
with characteristic $0$ and let $\sigma _b(X)$ be the $b$-secant variety of
$X$. We prove that the $X$-rank of $q$ is at least $b+1$ for a non-empty
codimension $1$ locally closed subset of $\sigma _b(X)$.
