Through the data around 3 GHz from the Radio Spectrometer in Huairou, Beijing, zebra-pattern structures from the 21 April 2002 event have been studied. Zebra stripes consist of periodically pulsating superfine structures in this event. An analysis of temporal profiles of intensities at multiple frequency channels shows that the Gaussian temporal profiles of pulse groups on zebra stripes are caused by drifting zebra stripes with Gaussian spectral profiles. The observed quasiperiodic pulsations with about 30 ms period have a peculiar feature of oscillation near a steady state, probably resulting from relaxation oscillations, which modulate the electron cyclotron maser emission that forms the zebra stripes during the process of wave particle interactions. All the main properties of the zebra stripes with pulsating superfine structures indicate that the double plasma resonance model might be the most suitable one, with the relaxation oscillations, to form the superfine structures. The model of LaBelle et al. ( Astrophys. J. 593, 1195, 2003) could not account for the observed properties of zebra-pattern structures in this event nor for most zebra-pattern structures occupying a wide frequency range, mainly because the allowable frequency range of the zebra-pattern structures in their model is too narrow to reproduce the observed zebras.