let $p$ be a prime number greater than three. in this paper, we prove the existence of a new family of homotopy elements in the stable homotopy groups of spheres $pi_{ast}(s)$ which is represented by $h_nh_mtilde{beta}_{s+2}in {rm ext}_a^{s+4, q[p^n+p^m+(s+2)p+(s+1)]+s}(mathbb{z}_p,mathbb{z}_p)$ up to nonzero scalar in the adams spectral sequence, where $ngeq m+2>5$, $0leq sext}_a^{s+2,q[(s+2)p...