  In this work we prove that the local $\gamma$-factor arising from the
doubling integrals for split general spin groups is stable. This deep property
of the $\gamma$-factor constitutes an important ingredient in the application
of the (generalized) doubling method to the construction of a global functorial
lift. We obtain our result by adapting the arguments of Rallis and Soudry who
proved the stability property for symplectic and orthogonal groups.
