  We study non-paraSasakian paracontact metric $(\kappa,\mu)$-spaces with
$\kappa=-1$ (equivalent to $h^2=0$ but $h\neq0$). These manifolds, which do not
have a contact geometry counterpart, will be classified locally in terms of the
rank of $h$. We will also give explicit examples of every possible constant
rank of $h$.
