The identification of a set of relevant but not redundant features is an important first step in building predictive and diagnostic models from biomedical data sets. Most commonly, individual features are ranked in terms of a quality criterion, out of which the best (first) k features are selected. However, feature ranking methods do not sufficiently account for interactions and correlations between the features. Thus, redundancy is likely to be encountered in the selected features. We present a new algorithm, termed Redundancy Demoting (RD), that takes an arbitrary feature ranking as input, and improves this ranking by identifying redundant features and demoting them to positions in the ranking in which they are not redundant. Redundant features are those that are correlated with other features and not relevant in the sense that they do not improve the discriminatory ability of a set of features. Experiments on two cancer data sets, one melanoma image data set and one lung cancer microarray data set, show that our algorithm greatly improves the feature rankings provided by the methods information gain, ReliefF and Student's t-test in terms of predictive power.