We present high-time-resolution spectroscopy of the non-eclipsing old nova V533 Herculis (N Her 1963). It is the second nova remnant affected by the `SW Sex syndrome'. A modulation of the equivalent width of the emission lines with a period of 23.33 min has been detected. This, together with the strong He IIλ4686 emission characteristic of magnetic systems, leads us to link this period to the spin of a magnetic white dwarf. Similar flaring activity has been recorded in other SW Sex stars, namely, the old nova BT Mon, LS Peg and DW UMa, supporting the idea of these systems being magnetic accretors. Stationary emission features are also observed in the Balmer lines, which we attribute to the ejected nova shell.