We show that the low density regions of the matter distribution preserve the properties of the primordial density field better than the high density regions. We have performed a cosmological N-body simulation of large-scale structure formation in the standard CDM cosmology, and studied the evolution of statistics of under-density and over-density regions separately. The rank-order of the under-density regions is closer to the original one compared to that of the over-density regions. The under-density peaks (or voids) has moved less than over-density peaks (or dense clusters of galaxies) from their initial positions. Therefore, the under-density regions are more useful than the over-density regions in the study of the statistical property of the primordial density field.