  We introduce a special class of nilpotent Lie groups of step 2, that
generalizes the so called $H$(eisenberg)-type groups, defined by A. Kaplan in
1980. We change the presence of inner product to an arbitrary scalar product
and relate the construction to the composition of quadratic forms. We present
the geodesic equation for sub-semi-Riemannian metric on nilpotent Lie groups of
step 2 and solve them for the case of general $H$-type groups. We also present
some results on sectional curvature and the Ricci tensor of general $H$-type
groups.
