Although wavelet-based steganography techniques are widely used due to their advantages, complete embedding data extraction remains one of the most significant challenges in this field. The Integer Wavelet Transform (IWT) can reduce extraction errors by mapping the image to integers, but it does not fully eliminate them. The proposed method resolves these errors entirely by using an iterative embedding procedure. After determining the image blocks and performing the IWT, this method embeds data in high-frequency sub-bands coefficient pairs. Additionally, it modifies the coefficient pair values such that the XOR of two coefficient LSBs equals two bits of data. The genetic algorithm is used to generate new coefficient values in order to minimize the differences between the stego and cover images. The sender repeats the embedding operation on each block until all extraction errors have been eliminated. If this procedure is unsuccessful in a block, the sender signs it as empty block. The results of the implementation suggest that with each iteration, the errors typically diminish to zero in most of the blocks. Further examination of the test results shows an enhancement in the PSNR and SSIM metrics when contrasted with existing methods. Moreover, the test results also expose the inability of attacks to uncover this method. Key merits of the proposed method include its superior stego image quality, substantial security against attacks, no requirement for lengthy keys, and a zero extraction error rate. These features render this method highly viable for practical applications.