We present evidence for a morphological segregation of early-type galaxies with different isophote shapes in the Virgo cluster. Comparing local projected densities around galaxies, we find that, independently of their classification as elliptical or lenticular, galaxies with boxy isophotes are located in local density enhancements, while galaxies with discy isophotes lie in regions of lower local densities. This segregation is therefore not just the reflection of ordinary morphological segregation between elliptical and lenticular galaxies, and it shows that the property of galaxies that is more sensitive to the environment is the presence or not of a stellar disc, rather than the bulge-to-disco ratio (and therefore the classification as an E or an S0 galaxy).