A secure method for steganography is proposed. Pixel-value differencing (PVD) steganography and bit-plane complexity segmentation (BPCS) steganography have the weakness of generating blocky effects and noise in smooth areas and being detectable with steganalysis. To overcome these weaknesses, a secure bit-plane based steganography method on the spatial domain is presented, which uses a robust measure to select noisy blocks for embedding messages. A matrix embedding technique is also applied to reduce the change of cover images. Given that the statistical property of cover images is well preserved in stego-images, the proposed method is undetectable by steganalysis that uses RS analysis or histogram-based analysis. The proposed method is compared with the PVD and BPCS steganography methods. Experimental results confirm that the proposed method is secure against potential attacks.