In this paper, we discuss in depth, one of the basic procedures that stands behind probabilistic seismic-hazard analysis (PSHA), that is, the declustering of the seismicity rates. First, we explore the technical, scientific, and practical motivations that led to introducing the declustering of seismicity rates. Then, we show that for PSHA, declustering is essential only to minimize a spatial distortion of the earthquake occurrence process, but, conversely, it may lead to significant underestimation of the true seismic hazard. This underestimation precludes the possibility to test meaningfully PSHA against real observations, and it may lead to underestimate the seismic risk, whenever seismic-hazard maps are used for risk assessment. Finally, we propose a methodology that can be used in PSHA to avoid this potential bias.