In this paper, using a new steganalytic method, namely the left-and-right cube analysis (LRCA), we explore the steganography exploiting the JPEG2000 image as the carrier medium, where the steganography works by substituting message bits for the least significant bits (LSBs) of the quantized wavelet coefficients. For the achievement of the LRCA implementation on JPEG2000 images, we establish an appropriate sampling rule to extract the sample vectors from the image data,
the quantized wavelet coefficients, in the wavelet domain. In experiments, we used the LSB steganography and the bit-plane complexity segmentation (BPCS) steganography in order to generate the stego images. In results, the proposed method works well for both steganographic methods, and outperforms some other previous steganalytic methods.