Based on some simple arithmetic operation, an efficient lossless image compression technique is proposed We use repeat reduction and arithmetic coding to improve the results of compression. We get better results than Log-Exp based compression and Arithmetic modulo based compression. From the experimental results, it can be seen that the performance ofproposed method is better for all standard images. The complexity of our proposed method with respect to compression ratio has also been analyzed The proposed method is most applicable for those images where lossy compression is to be avoided