Abstract: Twin support vector machine (TWSVM for short), as a variant of GEPSVM, is based on the idea of generalized support vector machine (GEPSVM), which determines two nonparallel planes by solving two related SVMtype problems, such that its computing cost in the training phase is 1/4 of standard SVM. In addition to keeping the superior characteristics of GEPSVM, classification performance of TWSVM significantly outperforms that of GEPSVM. However, the standalone method requires the solution of two smaller quadratic programming problems (QPPs) and there are few modifications of it that have been proposed to automatically select the input features. In this paper, through introducing a regularization term to the objective functions of TWSVM pair, the authors first propose a modification of TWSVM, called RTWSVM. Entirely different formulation from TWSVM, RTWSVM guarantees two QPPs are strong convex, implying that it can obtain the global but unique solution. Then, a feature selection method for RTWSVM is proposed, which is based on RTWSVM, and generates two planes directly from solving two sets of linear equations and requires no special optimization solvers. This method can obtain comparable classification performance to TWSVM, and have faster computational time, better suppression of input features and better ability to reduce the number of kernel functions.