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Feature selection has drawn much attention over the last decades in machine learning because it can reduce data dimensionality while maintaining the original physical meaning of features, which enables better interpretability than feature extraction. However, most existing feature selection approaches, especially deep-learning-based, often focus on the features with great importance scores only but neglect those with less importance scores during training as well as the order of important candidate features. This can be risky since some important and relevant features might be unfortunately ignored during training, leading to suboptimal solutions or misleading selections. In our work, we deal with feature selection by exploiting the features with less importance scores and propose a feature selection framework based on a novel complementary feature mask. Our method is generic and can be easily integrated into existing deep-learning-based feature selection approaches to improve their performance as well. Experiments have been conducted on benchmarking datasets and shown that the proposed method can select more representative and informative features than the state of the art.