This paper proposes a near-lossless image compression scheme which is based on both the replacement of random noise with a predictable pattern and the lossless binary image compression of bit-planes. Random noise on the binary image prevents from achieving at high compression ratio. A solution is to replace the random noise with a predictable pattern. Squared-local regions like random noise are replaced with a checker board pattern, Random noise on the upper bit-planes is stored. Random noise on the lower bit-planes is not stored but generated by pseudo-random number in decoding because the lower bit-planes have no significant information.