  The Fr\"olicher spectral sequence of a compact complex manifold $X$ measures
the difference between Dolbeault cohomology and de Rham cohomology.
  We construct for $n\geq 2$ nilmanifolds with left-invariant complex structure
$X_n$ such that the $n$-th differential $d_n$ does not vanish. This replaces an
earlier incorrect example by the second author.
