Pulsars provide unique probes of the large-scale interstellar magnetic field in the Galactic disk . Up to now , the limited Galactic distribution of the known pulsar population has restricted these investigations to within a few kiloparsec of the Sun . The Parkes multibeam pulsar survey has discovered many more-distant pulsars which enables us for the first time to explore the magnetic field in most of the nearby half of the Galactic disk . Here we report the detection of counterclockwise magnetic fields in the Norma spiral arm using pulsar rotation measures . The fields are coherent in direction over a linear scale of \sim 5 kpc along the arm and have a strength of -4.4 \pm 0.9 \mu G. The magnetic field between the Carina-Sagittarius and Crux-Scutum arms is confirmed to be coherent from l \sim 45 \arcdeg to l \sim 305 \arcdeg over a length of \sim 10 kpc . These results strengthen arguments for a bisymmetric spiral model for the field configuration in the Galactic disk .