  The results of paper [1] are generalized for vacuum type-III solutions with,
in general, a non-vanishing cosmological constant Lambda. It is shown that all
curvature invariants containing derivatives of the Weyl tensor vanish if a
type-III spacetime admits a non-expanding and non-twisting null geodesic
congruence.
  A non-vanishing curvature invariant containing first derivatives of the Weyl
tensor is found in the case of type-III spacetime with expansion or twist.
