With the increasing use of the internet and the growing volume of exchanged data, it has become possible to store and send medical information about patients. On the other hand, the use of these methods poses significant risks to the privacy of patient information. Therefore, the use of information hiding techniques, in such a way that the information is not easily detectable or alterable, has become essential. One such method is steganography. In this paper, magnetic resonance imaging (MRI) images are used as hosts for steganographic operations. In the proposed method, all wavelet coefficients of the secret image are embedded in the coefficients of the host image using the suggested α relation. In the experiments conducted, the performance of the wavelet-based steganography in embedding the secret image coefficients into the approximation, horizontal, vertical, and diagonal detail coefficients of the host image at four wavelet decomposition levels are compared. The comparison is performed using the Mean Squared Error (MSE) and Signal to Noise Ratio (SNR) metrics. The results show that steganography at the fourth level of wavelet decomposition, with embedding in the diagonal details, provides the best outcome in terms of both visual and statistical quality.