The Southern Galactic Plane Survey ( SGPS ) is an H i and 1.4-GHz continuum survey of the 4th quadrant of the Galaxy at arcmin resolution . We present here results on linearly polarized continuum emission from an initial 28-square-degree Test Region for the SGPS , consisting of 190 mosaiced pointings of the Australia Telescope Compact Array , and covering the range 325 \fdg 5 < l < 332 \fdg 5 , -0 \fdg 5 < b < +3 \fdg 5 . Complicated extended structure is seen in linear polarization throughout the Test Region , almost all of which has no correlation with total intensity . We interpret the brightest regions of polarized emission as representing intrinsic structure in extended polarization , most likely originating in the Crux spiral arm at a distance of 3.5 kpc ; fainter polarized structure is imposed by Faraday rotation in foreground material . Two large areas in the field are devoid of polarization . We argue that these voids are produced by foreground H ii regions in which the magnetic field is disordered on scales of \sim 0.1 - 0.2 pc . We also identify a depolarized halo around the H ii region RCW 94 , which we suggest results from the interaction of the H ii region with a surrounding molecular cloud .