  We study the limiting behavior of extremal cohomology groups of $k$-points
configuration spaces of complex projective spaces of complex dimension $m\geq
4.$ In the previous work, we prove that the extremal cohomology groups of
degrees $(2m-2)k+i$ are eventually vanish for each $i\in\{1,2,3\}.$ In this
paper, we investigate the extremal cohomology groups for non-positive integers,
and show that these cohomology groups are eventually vanish for
$i\in\{-1,-2,0\}.$ As an application, we confirm the validity of more general
question of Knudsen, Miller and Tosteson for non-positive integers. We give a
certain families of unstable cohomology groups, which are not eventually
vanish. The degrees of these families of cohomology groups are depend on the
number of points and the dimension of projective spaces. We formulate the
conjecture that the cohomology groups of higher slopes are eventually vanish.
