Encoding multiple SIFT descriptors into a single vector is a key technique for efficient object image retrieval. In this paper, we propose an extension of local coordinate system (LCS) for image representation. The previous LCS approaches encode each SIFT descriptor by a single local coordinate, which is not adequate for localizing its position in the descriptor space. Instead, we use multiple local coordinates to represent each descriptor with PCA-based decorrelation. Experiments show that this simple modification can improve retrieval performance significantly.