We study the effect of the Dresselhaus spin-orbit interaction on the magnetoresistance (MR) of a
quasi-one-dimensional ferromagnetic semiconductor containing a sharp domain wall. The MR is calculated
in the ballistic regime, within the Landauer-B¨uttiker formalism. The results show that the Dresselhaus
spin-orbit coupling which induces an effective magnetic field along the wire, reduces the domain wall MR.