A new effect of double refraction in a coherent medium with a double-Λ scheme of excitation is analysed theoretically. It arises if usual phase conditions on coherent population trapping in a quantum system with closed interaction contour are satisfied. The value of the refractive index of such a medium is different for matched and antimatched (by amplitude) parts of a bichromatic laser radiation. Therefore the matched part can be separated spatially from the antimatched one using the optically thin coherent medium as a birefringent prism. A possible scheme for experimental observation of this effect is discussed.