With the widespread success of deep learning technologies, many trained deep neural network (DNN) models are now publicly available. However, directly reusing the public DNN models for new tasks often fails due to mismatching functionality or performance. Inspired by the notion of modularization and composition in software reuse, we investigate the possibility of improving the reusability of DNN models in a more fine-grained manner. Specifically, we propose two modularization approaches named CNNSplitter and GradSplitter, which can decompose a trained convolutional neural network (CNN) model for $N$-class classification into $N$ small reusable modules. Each module recognizes one of the $N$ classes and contains a part of the convolution kernels of the trained CNN model. Then, the resulting modules can be reused to patch existing CNN models or build new CNN models through composition. The main difference between CNNSplitter and GradSplitter lies in their search methods: the former relies on a genetic algorithm to explore search space, while the latter utilizes a gradient-based search method. Our experiments with three representative CNNs on three widely-used public datasets demonstrate the effectiveness of the proposed approaches. Compared with CNNSplitter, GradSplitter incurs less accuracy loss, produces much smaller modules (19.88% fewer kernels), and achieves better results on patching weak models. In particular, experiments on GradSplitter show that (1) by patching weak models, the average improvement in terms of precision, recall, and F1-score is 17.13%, 4.95%, and 11.47%, respectively, and (2) for a new task, compared with the models trained from scratch, reusing modules achieves similar accuracy (the average loss of accuracy is only 2.46%) without a costly training process. Our approaches provide a viable solution to the rapid development and improvement of CNN models.