  We develop the embedding formalism for odd dimensional Dirac spinors in AdS
and apply it to the (geodesic) Witten diagrams including fermionic degrees of
freedom. We first show that the geodesic Witten diagram (GWD) with fermion
exchange is equivalent to the conformal partial waves associated with the spin
one-half primary field. Then, we explicitly demonstrate the GWD decomposition
of the Witten diagram including the fermion exchange with the aid of the split
representation. The geodesic representation of CPW indeed gives the useful
basis for computing the Witten diagrams.
