Objective: Between-session non-stationarity is a major challenge of current Brain-Computer Interfaces (BCIs) that affects system performance. In this paper, we investigate the use of channel selection for reducing between-session non-stationarity with Riemannian BCI classifiers. We use the Riemannian geometry framework of covariance matrices due to its robustness and promising performances. Current Riemannian channel selection methods do not consider between-session non-stationarity and are usually tested on a single session. Here, we propose a new channel selection approach that specifically considers non-stationarity effects and is assessed on multi-session BCI data sets. Methods: We remove the least significant channels using a sequential floating backward selection search strategy. Our contributions include: 1) quantifying the non-stationarity effects on brain activity in multi-class problems by different criteria in a Riemannian framework and 2) a method to predict whether BCI performance can improve using channel selection. Results: We evaluate the proposed approaches on three multi-session and multi-class mental tasks (MT)-based BCI datasets. They could lead to significant improvements in performance as compared to using all channels for datasets affected by between-session non-stationarity and to significant superiority to the state-of-the-art Riemannian channel selection methods over all datasets, notably when selecting small channel set sizes. Conclusion: Reducing non-stationarity by channel selection could significantly improve Riemannian BCI classification accuracy. Significance: Our proposed channel selection approach contributes to make Riemannian BCI classifiers more robust to between-session non-stationarities.