In this paper, the wavelet image coder, that can encode the bit-level information of wavelet coefficients, is proposed. The proposed coder is used the modified EZW algorithm and significant coefficient array that has bit level information of the wavelet coefficients to reduce the memory requirement in coding process. The significant coefficient array is two dimensional data structure that has bit level information of the wavelet coefficients. The proposed algorithm performs the coding of the significance coefficients and coding of bit level information of wavelet coefficients at a time by using the significant coefficient array. Experimental results show a better or similar performance of the proposed method when compared with conventional embedded wavelet coding algorithm. Especially, the proposed algorithm performs stably without image distortion at various bit rates with minimum memory usage by using the significant coefficient array.