We analysed Rossi X-ray Timing Explorer Proportional Counter Array observations of a recent outburst of the X-ray pulsar XMMU J054134.7-682550. We calculated the pulse frequency history of the source. We found no sign of a binary companion. The source spins up when the X-ray flux is higher, with a correlation between the spin-up rate and X-ray flux, which may be interpreted as a sign of an accretion disc. On the other hand, the source was found to have an almost constant spin frequency when the X-ray flux is lower without any clear sign of a spin-down episode. The decrease in pulsed fraction with decreasing X-ray flux was interpreted as a sign of accretion geometry change, but we did not find any evidence of a transition from accretor to propeller regimes. The source was found to have variable pulse profiles. Two peaks in pulse profiles were usually observed. We studied the X-ray spectral evolution of the source throughout the observation. Pulse-phase-resolved analysis does not provide any further evidence for a cyclotron line, but may suggest a slight variation of intensity and width of the 6.4 keV iron line with phase.