On the basis of the geometrical optics limit of the Kirchhoff approximation we design a one-dimensional random interface between two dielectric media that refracts $p$- or $s$-polarized light incident on it at an arbitrary angle of incidence $\theta_0$ from one of them into the other at an arbitrary but specified angle of transmission $\theta_t$ that is not defined in terms of $\theta_0$ by Snell's law. We call such transmission {\it nonstandard refraction}.