We study germs of holomorphic mappings between general algebraic hypersurfaces. Our main result is the following. If $(M,p_0)$ and $(M^{\text{'}},p_0^{\text{'}})$ are two germs of real algebraic hypersurfaces in ${ℂ}^{N+1}$, $N\ge 1$, $M$ is not Levi-flat and $H$ is a germ at $p_0$ of a holomorphic mapping such that $H\left(M\right)\subseteq M^{\text{'}}$ and $\mathrm{Jac}\left(H\right)\not\equiv 0$ then the so-called reflection function associated to $H$ is always holomorphic algebraic. As a consequence, we obtain that if $M^{\text{'}}$ is given in the so-called normal form, the transversal component of $H$ is always algebraic. Another corollary of...