For a knot
K
K
in the
3
3
-sphere, by using the linking form on the first homology group of the double branched cover of the
3
3
-sphere, we investigate some numerical invariants,
4
4
-genus
g
∗
(
K
)
g^*(K)
, nonorientable
4
4
-genus
γ
∗
(
K
)
\gamma ^*(K)
and
4
4
-dimensional clasp number
c
∗
(
K
)
c^*(K)
, defined from the four-dimensional viewpoint. T. Shibuya gave an inequality
g
∗
(
K
)
≤
c
∗
(
K
)
g^*(K)\leq c^*(K)
, and asked whether the equality holds or not. From our result in this paper, we find that the equality does not hold in general.