Let R be a local Artin ring with maximal ideal $\frak m$ and residue class field of characteristic p > 0. We show that every finite flat group scheme over R is annihilated by its rank, whenever $\frak m$p = p$\frak m$ = 0. This implies that any finite flat group scheme over an Artin ring the square of whose maximal ideal is zero, is annihilated by its rank.