Feature extraction of data lying on disconnected manifold is an open problem in the field of manifold learning, and decomposition-composition (D-C) algorithm is the most effective method so far to deal with this problem. However, the biggest limitation of D-C method is edge problem, that is when the nearest data points of different clusters are located in the inner part instead of the edge part of the corresponding cluster, D-C method always behaves poorly. To tackle this key issue, a method, called transition curve method, is presented in this paper. The main idea of the method is to make all clusters on the underlying manifold connect more effectively by constructing smooth transition curves which connect the nearest edge points of different clusters, and in this way the global shape of the data can be preserved better in the low-dimensional space. Experimental results on a series of synthetic and image data sets verify that the transition curve method performs evidently better than D-C method. Particularlly, the edge problem is alleviated. In this way, the application scope of D-C method is expanded remarkably.