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Absolute Moment Block Truncation Coding (AMBTC) is one of the lossy image compression techniques. The computational complexity involved is less and the quality of the reconstructed images is appreciable. The normal AMBTC method requires 2 bits per pixel (bpp). In this paper, two novel ideas have been incorporated as part of AMBTC method to improve the coding efficiency. Generally, the quality degrades with the reduction in the bit-rate. But in the proposed method, the quality of the reconstructed image increases with the decrease in the bit-rate. The proposed method has been tested with standard images like Lena, Barbara, Bridge, Boats and Cameraman. The results obtained are better than that of the existing AMBTC method in terms of bit-rate and the quality of the reconstructed images.