Unsupervised feature selection based on spectral clustering mainly involves the correlation coefficient matrix and the clustering indicator matrix. In previous studies, scholars have mainly focused on the correlation coefficient matrix, designing a series of constraints and improvements for it. However, focusing solely on the correlation coefficient matrix cannot fully learn the intrinsic structure of data. Considering the group effect, this study imposes the F-norm on the clustering indicator matrix and combines it with spectral clustering to make the correlation coefficient matrix learn more accurate clustering indicator information. The two matrices are solved through an alternating iteration method. Experiments on different types of real datasets show the effectiveness of the proposed method. In addition, experiments show that the F-norm can also make the method more robust.