Invasive brain-computer interfaces yield remarkable performance in a multitude of applications. For classification experiments, high-gamma bandpower features and linear discriminant analysis (LDA) are commonly used due to simplicity and robustness. However, LDA is inherently static and not suited to account for transient information that is typically present in high-gamma features. To resolve this issue, we here present an extension of LDA to the time-variant feature space. We call this method time-variant linear discriminant analysis (TVLDA). It intrinsically provides a feature reduction stage, which makes external approaches thereto obsolete, such as feature selection techniques or common spatial patterns (CSPs). As well, we propose a time-domain whitening stage which equalizes the pronounced 1/f-shape of the typical brain-wave spectrum. We evaluated our proposed architecture based on recordings from 15 epilepsy patients with temporarily implanted subdural grids, who participated in additional research experiments besides clinical treatment. The experiments featured two different motor tasks involving three high-level gestures and individual finger movement. We used log-transformed bandpower features from the high-gamma band (50–300 Hz, excluding power-line harmonics) for classification. On average, whitening improved the classification performance by about 11%. On whitened data, TVLDA outperformed LDA with feature selection by 11.8%, LDA with CSPs by 13.9%, and regularized LDA with vectorized features by 16.4%. At the same time, TVLDA only required one or two internal features to achieve this. TVLDA provides stable results even if very few trials are available. It is easy to implement, fully automatic and deterministic. Due to its low complexity, TVLDA is suited for real-time brain-computer interfaces. Training is done in less than a second. TVLDA performed particularly well in experiments with data from high-density electrode arrays. For example, the three high-level gestures were correctly identified at a rate of 99% over all subjects. Similarly, the decoding accuracy of individual fingers was 96% on average over all subjects. To our knowledge, these mean accuracies are the highest ever reported for three-class and five-class motor-control BCIs.