Finding a subspace which consists of the most informative features for reliable hyperspectral image classification is a challenging task. Feature reduction is often achieved via feature selection and feature extraction techniques. In this letter, a hybrid approach which combines both treatments is proposed. Principal Component Analysis (PCA) is applied as a preprocessing step so that each of the new features is generated from the complete set of the original spectral bands. Feature selection is then performed effectively using a normalized Mutual Information (nMI) measure with two constraints to maximize general relevance and minimize redundancy in the selected subspace. The proposed algorithm (PCA-nMI) is tested on hyperspectral images and the experimental results show that the modifications give significant improvement in terms of classification accuracy.