In 2020, Oh and Thomas constructed a virtual cycle
[
X
]
v
i
r
∈
A
∗
(
X
)
[X]^{\mathrm {vir}} \in A_*(X)
for a quasi-projective moduli space
X
X
of stable sheaves or complexes over a Calabi-Yau 4-fold against which DT4 invariants may be defined as integrals of cohomology classes. In this paper, we prove that the virtual cycle localizes to the zero locus
X
(
σ
)
X(\sigma )
of an isotropic cosection
σ
\sigma
of the obstruction sheaf
O
b
X
Ob_X
of
X
X
and construct a localized virtual cycle
[
X
]
l
o
c
v
i
r
∈
A
∗
(
X
(
σ
)
)
[X]^{\mathrm {vir}} _\mathrm {loc}\in A_*(X(\sigma ))
. This is achieved by further localizing the Oh-Thomas class which localizes Edidin-Graham’s square root Euler class of a special orthogonal bundle. When the cosection
σ
\sigma
is surjective so that the virtual cycle vanishes, we construct a reduced virtual cycle
[
X
]
r
e
d
v
i
r
[X]^{\mathrm {vir}} _{\mathrm {red}}
. As an application, we prove DT4 vanishing results for hyperkähler 4-folds. All these results hold for virtual structure sheaves and K-theoretic DT4 invariants.