For scene classification, patch-level linear features do not always work as well as handcrafted features. In this paper, we present a new model to greatly improve the usefulness of linear features in classification by introducing covariance patterns. We analyze their properties, discuss the fundamental importance, and present a generative model to properly utilize them. With this set of covariance information, in our framework, even the most naive linear features that originally lack the vital ability in classification become powerful. Experiments show that the performance of our new covariance model based on linear features is comparable with or even better than handcrafted features in scene classification.