  We introduce a systematic method to produce left-invariant, non-Ricci-flat
Einstein metrics of indefinite signature on nice nilpotent Lie groups. On a
nice nilpotent Lie group, we give a simple algebraic characterization of
non-Ricci-flat left-invariant Einstein metrics in both the class of metrics for
which the nice basis is orthogonal and a more general class associated to order
two permutations of the nice basis.
  We obtain classifications in dimension 8 and, under the assumption that the
root matrix is surjective, dimension 9; moreover, we prove that Einstein
nilpotent Lie groups of nonzero scalar curvature exist in every dimension $\geq
8$.
