This document presents a new technique called H-AMBTC (Hadamard-Absolute Moment Block Truncation Coding) for lossy image steganography. H-AMBTC combines Hadamard transformation with AMBTC (Absolute Moment Block Truncation Coding) to compress cover images and conceal secret data within them. The document describes the H-AMBTC encoding and decoding algorithms and compares its performance using different block sizes (2x2, 4x4, 8x8, 16x16) based on PSNR values. Results show that 16x16 blocks provided the best PSNR for test images, indicating higher quality of the stego-images produced by the H-AMBTC technique compared to smaller block sizes