  In this Note, we define a class of stratified Lie groups of arbitrary step
(that are called ``groups of type $\star$'' throughout the paper), and we prove
that, in these groups, sets with constant intrinsic normal are vertical
halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic
perimeter in a group of type $\star$ is rectifiable in the intrinsic sense (De
Giorgi's rectifiability theorem). This result extends the previous one proved
by Franchi, Serapioni & Serra Cassano in step 2 groups.
