It is shown that for layered-inhomogeneous uniaxial media, at a given frequency, there is some distribution of parameters over the thickness of the layer such that reflection will be absent for a normally propagating extraordinary wave. A general theorem for constructing the nonreflecting profile in an arbitrary layered-inhomogeneous uniaxial medium is given. The results are applied to a wave propagation in an Epstein profile. The results also indicated that even small variations in the spatial dependence of the parameters of the medium can affect the reflection coefficient significantly. © 1985.