We propose a method to determine accurately the relative wave propagation parameters (apparent slowness and propagation azimuth) of a cluster of seismic events with similar waveforms recorded on a seismic array. This relative slowness estimate (RelSE) method is based on precise measurements of the delays among arrivals of different earthquakes to each of the array receivers. Delays are determined using interpolations of the cross-correlation functions of the earthquake waveforms. Accurate relative slowness vectors are estimated using a least squares fit of the observed delays to the delays corresponding to the arrivals of plane wave fronts. We tested the method using both synthetics and real data, in order to understand its resolution capabilities in presence of seismic noise and to assess the uncertainty regions associated with the slowness vector estimates. From these analyses, we establish a procedure to determine the 90% uncertainty regions associated with the estimates of relative slowness vectors. As an example of application of the RelSE method, we analyzed a multiplet composed of 16 similar earthquakes recorded during the 1999 seismic crisis at Deception Island volcano, Antarctica. Using a conventional slowness estimate method produces virtually the same result for every earthquake, because of the large uncertainties. Alternatively, using the RelSE method reduces the uncertainties of the estimates and allows to resolve the detailed distribution of (relative) apparent slowness vectors. Our results show that the slowness vectors are aligned within a narrow, north-south trending band, which represents a clue toward the features of the source region and/or source distribution. We repeated the procedure using different earthquakes as master events. The estimated distribution of slowness vectors is similar in every case, which demonstrates that our results are independent of the choice of reference event.