Electromagnetic sources in a uniaxial anisotropic medium are known to
be decomposable in two parts producing fields with TE and TM polarizat
ion with respect to the axis of the medium. Also, an expression for th
e Green dyadic in the same medium has been derived. In this study, the
se two solution principles are brought together by finding the TE/TM d
ecomposition of the Green dyadic. This is done by finding the solution
for the ensuing fourth-order partial differential equations in analyt
ic form. In addition to being conceptually attractive, the new decompo
sed expression is helpful in solving electromagnetic problems with eit
her TE or TM character, in which case only one of two components of th
e Green dyadic is needed.