  We have prepared crystallographically ordered and disorder specimens of the
double perovskite, Sr$_2$FeMoO$_6$ and investigated their magnetoresistance
behaviour. The extent of ordering between the Fe and Mo sites in the two
samples is determined by Rietveld analysis of powder x-ray diffraction patterns
and reconfirmed by M\"{o}ssbauer studies. While the ordered sample exhibits the
sharp low-field response, followed by moderate changes in the magnetoresistance
at higher fields, the disordered sample is characterised by the absence of the
spectacular low-field response. We argue that the low field response depends
crucially on the half-metallic ferromagnetism, while the high-field response
follows from the overall magnetic nature of the sample, even in absence of the
half-metallic state.
