regard to the linear model Y = XC +ε, E(ε) = 0, Cov(ε,ε) =σ²I possessing the prior information: E(C) = 0, Cov(C, C) =σ²₀I, This article gives a best method of selecting the principal components' numbers in the principal components estimate and presents an improved principal components estimate. Theoretically, we prove that the improved estimate is admissible amd that it is marked much letter than Least Square Estimate and is better than the principal components estimate in a sense of “average”error of mean square. Simulation verifies the inference above.