A hyperspectral image provides fine details about the scene under analysis, due to its multiple bands. However, the resulting high dimensionality in the feature space may render a classification task unreliable, mainly due to overfitting and the Hughes phenomenon. In order to attenuate such problems, one can resort to dimensionality reduction (DR). Thus, this paper proposes a new DR algorithm, which performs an unsupervised band selection technique following a clustering approach. More specifically, the data set was split into a predefined number of clusters, after which the bands were iteratively selected based on the parameters of a separating hyperplane, which provided the best separation in the feature space, in a one-versus-all scenario. Then, a fine-tuning of the initially selected bands took place based on the separability of clusters. A comparison with five other state-of-the-art frameworks shows that the proposed method achieved the best classification results in 60% of the experiments.