Vortex beams are plagued by the intrinsic chromaticity of the physical phenomenon used to generate them. To the authors' best knowledge, attempts to generate them in a broad spectral range remain quite scarce and limited in their results. Crystal optics and especially conical diffraction (CD) (or refraction) intrinsically create achromatic vortices. The vortex is created by a wavelength-independent topological charge, embedded directly in the Fresnel equations. However, for biaxial crystals of low crystallographic symmetry, which includes all crystals used practically for CD, the dispersion of the binormal axis creates a chromaticity effect. In this Letter, we propose a new way to compensate this dispersion of the binormal axis of a biaxial crystal in order to generate white-light vortex beams by CD in a 250 nm spectral range, covering almost all the visible range. The advantages of the ability to use CD in a wide spectral range vastly exceed the sole generation of vortex beams.