This paper proposes a novel robust twin extreme learning machine (RTELM) for binary classification. To enhance its performance and robustness, we introduce two key techniques: (1) An average weight technique that assigns larger weights to data points near the class center and smaller weights to those near the boundary, leveraging the intra-class distribution; and (2) an improved pre-selection point technique that selects only the top- $u$ sorted data points to mitigate the impact of noise and outliers. Furthermore, we extend RTELM by incorporating a manifold regularization term, resulting in the Lap-RTELM framework, which enhances data discriminability. Extensive experiments validate that both RTELM and Lap-RTELM achieve superior classification performance, robustness, and stability compared to traditional methods.