Selecting the relevant factors in a particular domain is of utmost interest in the machine learning community. This paper concerns the feature selection process for twin support vector machine (TWSVM), a powerful classification method that constructs two nonparallel hyperplanes in order to define a classification rule. Besides the Euclidean norm, our proposal includes a second regularizer that aims at eliminating variables in both twin hyperplanes in a synchronized fashion. The baseline classifier is a twin SVM implementation based on second order cone programMing, which confers robustness to the approach and leads to potentially better predictive performance compared to the standard TWSVM formulation. The proposal is studied empirically and compared with well-known feature selection methods using microarray datasets, on which it succeeds at finding low dimensional solutions with highest average performance among all the other methods studied in this work.