Let $\Gamma$ be an algebraic curve determined over a finite field $k=[q]$; $e$, $\chi$ are subsidiary additive and multiplicative characters of the field $k$; $\varphi$, $\psi$ are functions in $\Gamma$ determined over $k$ and satisfying some natural conditions. If $P$ passes through the points of curve $\Gamma$, rational over $k$, then $$ \biggl|\sum_{P\in\Gamma}e(\varphi(P))\chi(\psi(P))\biggr|\leqslant C\sqrt q $$ where constant $C$ depends only on the powers of $\Gamma,\varphi,\psi$.