In this paper, the nontriviality of homotopy elements
β
1
ϱ
s
\beta _1\varrho _s
in the
p
p
-primary component of stable homotopy groups of spheres is shown by virtue of the Adams spectral sequence and the May spectral sequence, where
ϱ
s
\varrho _s
is represented by
b
0
g
0
γ
~
s
b_0g_{0}\widetilde {\gamma }_{s}
in the Adams spectral sequence,
p
p
is a prime number greater than
5
5
, and
3
≤
s
>
p
3\leq s>p
.