  Making use of the collinear expansion technique developed by Ellis, Furmanski
and Petrozio, and the special propagator concept invented by Qiu, we present a
factorization approach to the photon fragmentation tensor for the inclusive
Lambda hyperon production. As a result, the structure function $\tilde F$,
which is related to the transverse polarization of the inclusive Lambda hyperon
in unpolarized electron-positron annihilation, is expressed as a combination of
four parton fragmentation matrix elements. Since the inclusive $\Lambda$
production we considered is theoretically the simplest, our study can be taken
as a question to the operatability and practability of the first nonleading QCD
factorization theorem in the transverse $\Lambda$ polarization phenomena.
