Let E_1~r×E_2~r×E_3~r be the product of three euclidean cells and let f_i∈a_i∈π_(ri)(X),i=1,2,3.If the Whitehead products [α_1,α_2],α_2,α_3] and [α_1,α_3] aretrivial,there exist extensions φ_1:E_2~r×E_3~r→X,φ_2:E_l~rxE_3~r→X,and φ_3:E_1~r×E_2~r→X of the Whitehead products [f_2,f_3],[f_1,f_3] and [f_1,f_2] respectively.Define a mapF:(E_1~r×E_2~r×E_3~r)→Xsuch thatF(x×y×z)=φ_1(y×z),if x∈(?)_1~r,y∈E_2~r,z∈E_3~r,=φ_2(x×z),if x∈E_1~r,y∈(?)_2,z∈E_3~r,=φ_3(x×y),if x∈E_1~r,y∈(?)_2,z∈(?)_3~r.The map F contributes an element in π_(r1+r2+r3-1)(X),namely[φ_1,φ_2,φ_3]. Let Y be the topological space obtained from S_1~r×S_2~r×S_3~r by removingthe top dimensional cell.Let ψ_i(i=1,2,3)denote the characteristic maps ofthe r_2+r_3,r_1+r_3 and r_1+r_2 dimensional cells of Y respectively.Then it isproved thatπ_(r_1+r_2+r_3-1)(Y)=π_(r_1+r_2+r_3-1)(S_1~r)+π_(r_1+r_2+r_3-1)(S_2~r)+π_(r_1+r_2+r_3-1)(S_3~r)+[Ψ_1,Ψ_2,Ψ_3],where the sign+denotes direct summation and [ψ_1,ψ_2,ψ_3] is a free groupgenerated by one generator only.In the space X there may be another extension φ' of [f_2,f_3](=0).Thenit is proved that[φ_1,φ_2,φ_3]=[φ_1~',φ_2,φ_3]+∈[f_1,d(φ_1,φ_1~')],∈being+1 or-1 determined by the orientation concerned.The complexes {S~p×S~q} and S~p×S~q are distinguished by their p+q dimen-sional cells e~(p+q) and e_1~(p+q) only.The injectionj:S~p×S~q,S~p∪S~q→{S~p×s~q}∪e_1~(p+q),{S~p×S~q}induces the homomorphismε_(r+1):π_(r+1)(S~p×S~q,S~p∪S~q)→π_(r+1)({S~p×S~q}∪e_1~(p+q),{S~p×S~q}).Here ε_(2(p+q)-2)~(-1)(0) is proved to be at most a 2-group,if p+q is even.Parti-cularly,ε_(2(p+q)-2)is an isomorphism onto if p+q=4 or δ.In virtue of thearguments in[1]together with the new technique about[φ_1,φ_2,φ_3],the authorcalculatedπ_5(S~2∪S~2)and π_(13)(S~p∪S~(8-p)).They areπ_(4r-3)(S~r∪S~r)=π_(4r-3)(S~r)+π_(4r-3)(S~r)+π_(4r-2)(S~(2r))+π_(4r-1)(S~(3p))+π_(4r-1)(S~3p)+π_(4r)(S~(4p))+π_(4r)(S~(4p))+π+(4r)(S~(4p)),if r=2 or 4,andπ_(13)(S~p∪S~(8-p))=π_(13)(S~p)+π_(13)(S~(8-p))+π_(14)(S~8)+π_(15)(S~(8-p))+π_(16)(S~16)+sum from i=0 to ∞π_(16+i)(S~(16-p+i(8-p))),p=5 or 6.