In this paper, we introduce a new class of contact pseudo framed (CPF)-manifolds
M
,
g
,
f
,
λ
,
ξ
by a real tensor field
f
of type
1,1
, a real function
λ
such that
f
3
=
λ
2
f
where
ξ
is its characteristic vector field. We prove in our main Theorem 2 that
M
admits a closed 2-form
Ω
if
λ
is constant. In 1976, Blair proved that the vector field
ξ
of a normal contact manifold is Killing. Contrary to this, we have shown in Theorem 2 that, in general,
ξ
of a normal CPF-manifold is non-Killing. We also have established a link of CPF-hypersurfaces with curvature, affine, conformal collineations symmetries, and almost Ricci soliton manifolds, supported by three applications. Contrary to the odd-dimensional contact manifolds, we construct several examples of even- and odd-dimensional semi-Riemannian and lightlike CPF-manifolds and propose two problems for further consideration.