Abstract: Consider the linear model: Y_i=(y₁ⁱ,…,y_nⁱ)’=β+ε_i=（β₁,…, β_n）＇+(ε₁ⁱ…,ε_nⁱ)＇ i=1,…,m where Y₁,…, Y_m are independent, E （ε_i）=0, Var （ε_i）=σ_i²V,i= 1,…, m. β∈Rⁿ, 0＜σ_i²＜ ∞ unknown. The necessary and sufficient conditions that \sum_i=1^m A_i Y_i and \sum_i=1^m A_t Y_i+O are admissible for Sβ within the classes \sum_i=1^m A_i Y_i ; A_i: s \times n and \sum_i=1^m A_i Y_i+C; A_i: s×n,C:s×1 are given respectively. In comparision with the method used in other papers, we use the method of matrix derivative.