Gene selection (feature selection) is generally performed in gene space (feature space), where a very serious curse of dimensionality problem always exists because the number of genes is much larger than the number of samples in gene space (G-space). This results in difficulty in modeling the data set in this space and the low confidence of the result of gene selection. How to find a gene subset in this case is a challenging subject. In this paper, the above G-space is transformed into its dual space, referred to as class space (C-space) such that the number of dimensions is the very number of classes of the samples in G-space and the number of samples in C-space is the number of genes in G-space. It is obvious that the curse of dimensionality in C-space does not exist. A new gene selection method which is based on the principle of separating different classes as far as possible is presented with the help of Principal Component Analysis (PCA). The experimental results on gene selection for real data set are evaluated with Fisher criterion, weighted Fisher criterion as well as leave-one-out cross validation, showing that the method presented here is effective and efficient.