In order to eliminate the defect of successively separative calculations of different end-members of a min-eral and to establish a widely applicable new scheme for calculating mineral end-members, the use of the linearprogramming technique is proposed to calculate simultaneously all end-members in this paper. All calculationswith the scheme under study can result in non-negative values. In the case of calculating end-members ofclinopyroxene, the Eskola's molecule is introduced so as to reach stoichiometry. When certain minor elementsin solid solutions are present in a remarkable amount, by adding to the equations the vectors of the corre-sponding end-members and adjusting the component vectors it is possible to obtain calculation results, in-cluding those of such end-mempbers. The possibility of using the calculation scheme under study to estimate theFe~(3+)/Fe~(2+) ratio of a mineral from electron microprobe analysis is also discussed in this paper.