Abstract: Consider the following stable secondary cohomology operations associated with the relations in the mod 2 Steenrod algebra: such that Let ψ 5 be a stable tertiary cohomology operation associated with the above relation. We assume that (ϕ 4 , ϕ 5 ) and ψ 5 are chosen to be spin trivial in the sense of Theorem 3.7 of [ 14 ]. Let ϕ 0,0 , ϕ 1,1 be the stable Adams basic secondary cohomology operations associated with the relations: respectively.