Examples of naturally reductive pseudo-Riemannian Lie groups

We provide examples of naturally reductive pseudo-Riemannian spaces, in particular an example of a naturally reductive pseudo-Riemannian 2-step nilpotent Lie group $(N,<,{>}_N)$, such that $<,{>}_N$ is invariant under a left action and for which the center is degenerate. The metric does not correspond to a bi-invariant one.