The available formulation of Green's function for uniaxial dielectric anisotropic media features an apparent singularity on the medium's distinguished axis.However, following the physical understanding of the medium, we show that Green's function is, in fact, only singular in the source region.Doing so, we present an alternative derivation of Green's function, including its value along the distinguished axis.Finally, we provide a formula to describe the singular behavior of derivatives of singular functions.