Although seismic amplitudes can be used to estimate event locations for volcanic tremors and other seismic events with unclear phase arrival times, the precision of such estimates is strongly affected by site amplification factors. Therefore, reduction of the influence of site amplification will allow more precise estimation of event locations by this method. Here, we propose a new method to estimate relative event locations using seismic amplitudes. We use the amplitude ratio between two seismic events at a given station to cancel out the effect of the site amplification factor at that station. By assuming that the difference between the hypocentral distances of these events is much smaller than their hypocentral distances themselves, we derive a system of linear equations for the differences in relative event locations. This formulation is similar to that of a master event location method that uses differences in phase arrival times. We applied our new method to earthquakes and tremors at Meakandake volcano, eastern Hokkaido, Japan. Comparison of the hypocentral distributions of volcano-tectonic earthquakes obtained thereby with those obtained from phase arrival times confirmed the validity of our new method. Moreover, our method clearly identified source migration among three source regions in the tremor on 16 November 2008, consistent with previous interpretations of other geophysical observations in our study area. Our method will thus be useful for detailed analyses of seismic events whose onset times are ambiguous.