The phenomenon of superconductivity continues to be of considerable scientific and practical interest. Underlying this phenomenon is the formation of electron pairs, which in conventional superconductors do not rotate about their centre of mass ('s-wave' pairing; refs 1, 2). This contrasts with the situation in high-temperature superconductors, where the electrons in a pair are believed to have two units of relative angular momentum ('d-wave' pairing; ref. 3 and references therein), Here we report small-angle neutron-scattering measurements of magnetic nux lines in the perovskite superconductor Sr2RuO4 (ref. 4), which is a candidate for another unconventional paired electron state-'p-wave' pairing, which has one unit of angular momentum(5-7). We find that the magnetic flux lines form a square lattice over a wide range of fields and temperatures, which is the result predicted by a recent theory(8,9) of p-wave superconductivity in Sr2RuO4. This theory also indicates that only a fraction of the electrons are strongly paired and that the orientation of the square nux lattice relative to the crystal lattice will determine which parts of the three-sheet Fermi surface of this material are responsible for superconductivity. Our results suggest that superconductivity resides mainly on the `gamma' sheet(9).