Block truncation coding (BTC) is a successful image compression technique due to its simple and fast computational burden. The bit rate is fixed to 2.0 bits/pixel, whose performance is moderate in terms of compression ratio compared to other compression schemes such as discrete cosine transform (DCT), vector quantization (VQ), wavelet transform coding (WTC), etc. Two kinds of overheads are required for BTC coding: bit plane and quantization values, respectively. A new technique is presented to reduce the bit plane overhead. Conventional bit plane overhead is 1.0 bits/pixel; we decrease it to 0.734 bits/pixel while maintaining the same decoded quality as absolute moment BTC (AMBTC) does for the "Lena" image. Compared to other published bit plane coding strategies, the proposed method outperforms all of the existing methods.