A different and efficient method of image hiding is proposed here. It is based on unitary similarity transformation, involving calculation of eigen values and eigen vectors of a matrix and then transforming it into a diagonal matrix. Only secret image needs to be transformed and is then embedded to the cover image. Inverse transformation can be used to recover the secret image from the stego-image. The eigen vector matrix acts as decryption key. This algorithm is simple and can be easily implemented. It can greatly improve the security of the system, robustness of image-hiding. The quality of stego-image and the recovered image is improved up to a certain extent and is evident from the high PSNR of stego image.