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Let  p  be a prime with  p  ≥ 7 and  q =2( p -1). In this paper we prove the existence of a nontrivial product of filtration  p  + 2 in the stable homotopy groups of spheresπ   (   p  n   +   p  3   -  p  -  2  )  q  -  6    S    ${\pi _{(p^{n}+p^{3}-p-2)q-6}S}$   . This nontrivial product is shown to be represented up to a nonzero scalar by the product elementγ  ˜    p  -  1h  0    b   n  -  1    ∈    Extp  +  2  ,  (   p  n   +   p  3   -  p  -  2  )  q  +  p  -  4(  ℤ  /  p  ,  ℤ  /  p  )$ {\protect \widetilde{\gamma }_{p-1}h_{0}b_{n-1}\in {\rm Ext}_{\mathcal {A}}^{p+2,(p^{n}+p^{3}-p-2)q+p-4}(\mathbb {Z}/p,\mathbb {Z}/p)} $    in the Adams spectral sequence where  n  ≥ 1 and  n  ≥ 4.

The convergence of the product γ˜ p -1 h 0 b n -1 in the Adams spectral sequence