Let M be a real-analytic submanifold of ${ℂ}^n$ whose “microlocal” Levi form has constant rank $s_M^{+}+s_M^{-}$ in a neighborhood of a prescribed conormal. Then local non-solvability of the tangential ∂̅-system is proved for forms of degrees $s_M^{-}$, $s_M^{+}$ (and 0).  This phenomenon is known in the literature as “absence of the Poincaré Lemma” and was already proved in case the Levi form is non-degenerate (i.e. $s_M^{-}+s_M^{+}=n-codimM$). We owe its proof to [2] and [1] in the case of a hypersurface and of a higher-codimensional submanifold respectively....