This paper proposes a class of linear models with inequable variance, based on background in genetic linkage analysis, and considers the optimal design problem for the hypothesis test of the parameters in such models. To assess a design for the test, a frame of decision theory is established. Under this frame, an admissible minimax design is obtained. It is shown to be not only admissible and minimax in genetic linkage analysis, but best among a reasonable subclass of designs. The power of the test in genetic linkage analysis is substantially improved by using this optimal design.