In this work, a band selection technique based on FDA and functional PCA is proposed. The method selects shape-preserving, discriminative bands which can highlight the important characteristics, variations as well as patterns of the hyperspectral data such that the differences between data from different classes become more apparent. The selection is performed in two stages. The first stage is selection of shape-preserving, keypoint bands which explain the trend characteristics of the reflectance curves in the hyperspectral data. These bands are able to preserve the functional representation of the curves as close as possible to their original representation using all the bands. The second stage involves selection of bands with good discriminative capabilities from the previously selected keypoint bands. For this, a novel iterative band selection technique using supervised functional principal component analysis (SFPCA) is proposed. The proposed band selection algorithm is the first approach reported in literature to explore the functional behaviour of HSI. An objective comparison of the proposed approach with several widely used, state-of-art band selection methods demonstrate a significant improvement in the classification accuracy.